Intersection of 2 Lines in R^3Programmers: Raquel Belnap & Farhan SiddiquiMath 253 Honors Section 202Fall 2012Instructor: Philip Yasskin###################################
# # Header For All Maplets
restart:
with(Maplets[Elements]):
with(Maplets[Tools]):
StartEngine():
randomize():lightorange:="#FFB300":lightcyan:="#DDFFFF":lightblue:="#CFCFFF":lightgreen:="#CCFFCC":darkgreen:="#00C000":ColorBkgd:=wheat:ColorDefaultMenu:=lightcyan:ColorHelpMenu:=lightorange:ColorFileMenu:=pink:ColorFooter:=lightcyan:ColorNewButton:=magenta: # or Make, Save, Enter ProblemColorReturnButton:=magenta:ColorCloseButton:=pink: # or Quit, Clear, Reset, CancelColorHintButton:=lightorange: # or SyntaxColorPrevButton:=turquoise: # or UpdateColorEnterButton:=turquoise:ColorSimplifyButton:=lightorange:ColorCheckButton:=green:ColorShowButton:=yellow:ColorPlotButton:=gold: ColorPlotButtonFrgd:=black:ColorPlotFrame:=gold:ColorTableBkgd:=lightgreen:ColorCalculatorBkgd:=gold:ColorBlackBox:=black: ColorBlackBoxFrgd:=yellow:ColorMessage:=white: ColorMessageFrgd:=black:ColorInput:=turquoise: ColorInputFrgd:=black:ColorCorrect:=green: ColorCorrectFrgd:=black:ColorIncorrect:=red: ColorIncorrectFrgd:=white:ColorWarning:=yellow: ColorWarningFrgd:=black:ColorShow:=yellow: ColorShowFrgd:=black:ColorHint:=lightorange: ColorHintFrgd:=black: # or Info, SyntaxColorDisable:=wheat: ColorDisableFrgd:=black:FontFooter:=Font("helvetica",10):FontSymbol:=Font("symbol",12):FontBig:=Font("times",20):LIBLogo:=cat(libname,"/M4C/M4C.png"):Logo:="M4C.png":#LIBLogo:=cat(libname,"/M4C/WebALT_logo.png"):#Logo:="WebALT_logo.png":# ################################### # Template Translation Table For All MapletsTEXTLprogrammers:="Programmers: D.B. Meade & P.B. Yasskin":TEXTLcopyright:="\302\251 Copyright: Maplets for Calculus 2004-10":#"\302\251 Copyright: WebALT 2006-07":TEXTLversion:="M4C v1.3 July 2010":TEXTBQuit:="Quit":TEXTBClose:="Close":TEXTBCheck:="Check":TEXTBShow:="Show":TEXTBShowAll:="Show All Steps":TEXTBCheckAns:="Check Answer":TEXTBShowAns:="Show Answer":TEXTBInstructions:="Instructions":TEXTBHint:="Hint":TEXTBHints:="Hints":TEXTBSyntax:="Syntax":TEXTBHintSyntax:="Hints and Syntax":TEXTBPrev:="Preview":TEXTBUpdate:="Update":TEXTBDerivation:="Derivation":TEXTBNewProblem:="New Problem":TEXTBNewFunction:="New Function":TEXTBNewGraph:="New Graph":TEXTBNewEquation:="New Equation":TEXTBNewLimit:="New Limit":TEXTBNewDerivative:="New Derivative":TEXTBNewIntegral:="New Integral":TEXTBNewSequence:="New Sequence":TEXTBNewSeries:="New Series":TEXTBNewDiffEq:="New Differential Equation":TEXTBNewCurve:="New Curve":TEXTBEnterProblem:="Enter Problem":TEXTBEnterFunction:="Enter Function":TEXTBEnterGraph:="Enter Graph":TEXTBEnterEquation:="Enter Equation":TEXTBEnterLimit:="Enter Limit":TEXTBEnterDerivative:="Enter Derivative":TEXTBEnterIntegral:="Enter Integral":TEXTBEnterSequence:="Enter Sequence":TEXTBEnterSeries:="Enter Series":TEXTBEnterDiffEq:="Enter Differential Equation":TEXTBMake:="Modify or Make Your Own Problem":TEXTBSaveClose:="Save Problem and Close":TEXTBAskQuestion:="Ask Question":TEXTBNextQuestion:="Next Question":TEXTBHowtoAnswer:="How to Answer":TEXTBEnter:="Enter":TEXTBOK:="OK":TEXTBAccept:="Accept":TEXTBReturn:="Return":TEXTBClear:="Clear":TEXTBClearSelections:="Clear Selections":TEXTBClearAll:="Clear All Steps":TEXTBReset:="Reset":TEXTBRestart:="Restart":TEXTBCancel:="Cancel":TEXTBPlot:="Plot":TEXTBPlotIt:="Plot It":TEXTBAnimate:="Animate":TEXTBPlay:="Play":TEXTBPause:="Pause":TEXTBForward:="Forward":TEXTBReverse:="Reverse":TEXTBStep:="Step":TEXTBUpdatePlot:="Update Plot":TEXTBZoomIn:="Zoom In":TEXTBZoomOut:="Zoom Out":TEXTBPlotSetup:="Plot Setup":TEXTBRefresh:="Refresh":TEXTBCalculate:="Calculate":TEXTBSimplify:="Simplify":TEXTBFactor:="Factor":TEXTBExpand:="Expand":TEXTBNormalize:="Normalize":TEXTBCombine:="Combine":TEXTBRationalize:="Rationalize":TEXTBSort:="Sort":TEXTBDecimal:="Decimal":TEXTBExact:="Exact":TEXTCorrect:=" correct ":TEXTIncorrect:="incorrect":TEXTAlmost:=" almost ":TEXTWarning:=" warning ":TEXTShown:=" shown ":TEXTSlower:="Slower":TEXTFaster:="Faster":TEXTEnterFormula:=" Enter Formula:":TEXTEvaluate:=" Evaluate:":TEXTApproximate:=" Approximate:":TEXTand:=" and ":TEXTor:=" or ":TEXTThus:=" Thus ":TEXTSo:=" So ":TEXTType:=" Type ":TEXTfor:=" for ":TEXTat:=" at ":TEXTorcheck:=" or check: ":TEXTvertical:="vertical":TEXThorizontal:="horizontal":TEXTleft:="left":TEXTright:="right":TEXTless:="less":TEXTgreater:="greater":TEXTCBDNE:="does not exist":TEXTCBNone:="None":TEXTCB11scaling:="1-1 scaling":TEXTdefault:=" default ":TEXTCBDoNotShow:="Do not show this window again.":TEXTRBNumeric:="Numeric":TEXTRBSymbolic:="Symbolic":TEXTRBTrue:="True":TEXTRBFalse:="False":TEXTRBT:="T":TEXTRBF:="F":TEXTRBOn:="On":TEXTRBOff:="Off":TEXTRed:="Red":TEXTGreen:="Green":TEXTBlue:="Blue":TEXTCyan:="Cyan":TEXTMagenta:="Magenta":TEXTYellow:="Yellow":TEXTRedR:="R":TEXTGreenG:="G":TEXTBlueB:="B":TEXTRBPlot1:="Plot # 1":TEXTRBPlot2:="Plot # 2":TEXTRBPlot3:="Plot # 3":TEXTRBPlot4:="Plot # 4":TEXTRBPlot5:="Plot # 5":TEXTRBPlot6:="Plot # 6":TEXTRBconverge:="converge":TEXTRBdiverge:="diverge":TEXTRBconverges:="converges":TEXTRBdiverges:="diverges":TEXTRBdiverges2:="diverges ":TEXTRBconvergent:="Convergent":TEXTRBdivergent:="Divergent":TEXTtitlePROBLEM:="Modify or Make Your Own Problem":TEXTtitlePREVIEW:="Preview":TEXTtitleHINT:="Hint":TEXTtitleSYNTAX:="Syntax":TEXTtitlePlotSetup:="Plot Setup":TEXTCapGoal:="Goal:":TEXTCapProbStat:="Problem Statement:":TEXTCapSyntaxTutorial:="Syntax Tutorial:":TEXTCapEnter:="Enter:":TEXTCapSpecify:="Specify:":TEXTCapTrueFalse:="True or False?":TEXTCapCalculator:="Calculator":TEXTCapPlot:="Plot":TEXTCapLegend:="Legend":TEXTCapEvaluate:="Evaluate:":TEXTCapDataTable:="Data Table":TEXTCapVis:="Visualization":TEXTCapAnim:="Animation":TEXTCapPreviewer:="Previewer":TEXTCapHorRng:="Horizontal Range:":TEXTxmin:="xmin =":TEXTxmax:="xmax =":TEXTCapVertRng:="Vertical Range:":TEXTymin:="ymin =":TEXTymax:="ymax =":TEXTPlotWait:= #Use ColorHint" Please be patient while the plot is generated.":TEXTAnimWait:=" Please be patient while the animation is generated.":TEXTRotatePlot:=" You may rotate the plot with your mouse.":TEXTreplyNoCheck:=" You must enter an expression to be checked.":TEXTreplyNoCheckBoth:=" You must answer both questions before checking.":TEXTreplyNoChecks:=" You must answer all %a questions before checking.":TEXTreplyNoPrev:=" You must enter an expression to be previewed.":TEXTreplyNoSimplify:=" You must enter an expression to be simplified.":TEXTreplyNoFactor:=" You must enter an expression to be factored.":TEXTreplyNoExpand:=" You must enter an expression to be expanded.":TEXTreplyNoNormalize:=" You must enter an expression to be normalized.":TEXTreplyNoModify:=" You must enter an expression to be modified.":TEXTreplyNoPlot:=" Please select a plot.":TEXTreplyNoSelection:=" Please select an answer.":TEXTreplyNoSaveProblem:=" You must fill in all the boxes before saving the problem.":TEXTreplyNoSaveSettings:=" You must fill in all the boxes before saving the settings.":TEXTreplyNoSlider:=" Set the slider to a number between %a and %a":TEXTreplySideEqWrong:=" The %a side of your equation is wrong.":TEXTreplyBothSideEqWrong:=" Both sides of your equation are wrong.":TEXTreplySideIneqWrong:=" The %a side of your inequality is wrong.":TEXTreplyBothSideIneqWrong:=" Both sides of your inequality are wrong.":TEXTreplyNoConst:=" You forgot to add a constant of integration.":TEXTreplyManyConst:=" Your answer should have only one constant of integration.":TEXTreplyMinusErr:=" You have a minus sign error.":DNEset:={"", undefined, Undefined, UNDEFINED, divergent, Divergent, DIVERGENT, diverges, Diverges, DIVERGES, dne, DNE, doesnotexist, DoesNotExist}:TEXTM_File:="File":TEXTM_Fns:="Functions":TEXTCBMI_polygen:="Polynomials (Generalized)":TEXTCBMI_exp:="Exponentials":TEXTCBMI_log:="Logarithms":TEXTCBMI_trig:="Trigonometric":TEXTCBMI_invtrig:="Inverse Trigonometric":TEXTCBMI_hyper:="Hyperbolic":TEXTCBMI_invhyper:="Inverse Hyperbolic":TEXTCBMI_simpsubst:="Allow Simple Substitutions":TEXTM_Rules:="Rules":TEXTCBMI_prod:="Product Rule":TEXTCBMI_quot:="Quotient Rule":TEXTCBMI_power:="Power Rule":TEXTCBMI_chain:="Chain Rule":TEXTM_Methods:="Methods":TEXTCBMI_subst:="Substitution":TEXTCBMI_parts:="Integration by Parts":TEXTCBMI_trigpow:="Trigonometric Powers":TEXTCBMI_trigsubst:="Trigonometric Substitution":TEXTCBMI_trigident:="Trigonometric Identity":TEXTCBMI_parfrac:="Partial Fractions":TEXTCBMI_impfrac:="Improper Fraction":TEXTRBproper:="only proper integrals":TEXTRBimproper:="allow improper integrals":TEXTM_RulesProb:="Rules per Problem":TEXTreply_manyrules:=" Problems which involve too many rules tend to become rather messy.":TEXTM_MaxTerms:="Max # Terms":TEXTreply_manyterms:=" Problems with large numbers of terms tend to become rather messy.":TEXTM_TermsPoly:="Terms in Polynomial":TEXTM_PowerProp:="Power Properties":TEXTCBMI_neg:="Allow Negatives":TEXTCBMI_frac:="Allow Fractions":TEXTreply_largepower:=" Problems with large degree polynomials tend to become rather messy.":TEXTM_Help:="Help":TEXTmenu_start:="Getting Started":TEXTmenu_custom:="Customized Problems":TEXTmenu_manip:="Manipulating Functions":TEXTmenu_about:="About this maplet":great:=[" Bullseye."," Right on the mark."," Great."," That's absolutely right."," Awesome. You're unstoppable."," Correct."," WOW, nailed that one."," You got it!"," YES! Right on."," Way to go."," Don't stop now."," I knew you could do it!"," Perfect. You're unstoppable."," Radical Dude."," Power house."," Sweet! Keep on Rockin'."," You rock!"," You got those mad skills."," Awesome!"," Wowzers! That was great!"," Awesome man!"," Good job! You really know what you are doing."," You're awesome kid."," Tearing it up."," Right on the money."," High Five!!!!!"," Cool Beans."," What a nerd!"," You're so money."," You're a genius."," You hit the nail on the head."," Excellent!"," If I had a cookie, I'd give it to you."," You're a winner."," That's a winner."," Whoop! Way to go."," That's the way, ah ha ah ha, I like it."," Oh yeah!"," You're the bomb!"," That was fantastic!"," Oh Snap!",NULL]:nextgeneric:=[" Keep it up."," Keep going.",NULL]:nextprob:=[" On to the next problem."," Try another problem."," You're ready for another problem.",NULL]:nextquest:=[" On to the next question."," Try another question."," You're ready for another question.",NULL]:nextpart:=[" On to the next part."," Try another part."," You're ready for another part.",NULL]:nextstep:=[" On to the next step."," Try another step."," You're ready for another step.",NULL]:nexteq:=[" On to the next equation."," Try another equation."," Solve another equation."," You're ready for another equation.",NULL]:nextfn:=[" On to the next function."," Try another function."," You're ready for another function.",NULL]:nextlim:=[" On to the next limit."," Try another limit."," Compute another limit."," You're ready for another limit."," Find another limit.",NULL]:nextderiv:=[" On to the next derivative."," Try another derivative."," Compute another derivative."," You're ready for another derivative."," Differentiate another function.",NULL]:nextinteg:=[" On to the next integral."," Try another integral."," Compute another integral."," You're ready for another integral."," Integrate another function.",NULL]:nextdiffeq:=[" On to the next differential equation."," Try another differential equation."," You're ready for another differential equation."," Analyze another differential equation.",NULL]:nextseq:=[" On to the next sequence."," Try another sequence."," Find the limit of another sequence."," You're ready for another sequence.",NULL]:nextser:=[" On to the next series."," Try another series."," Sum another series."," You're ready for another series.",NULL]:almost:=[" Close."," Oh so close."," Close call. "," Near miss."," Not quite good enough for government work."," Ooooh...close."," Yikes! Really close. You'll get it next time."," Close, but no cigar."," Slightly off."," Off by a hair."," Almost there."," Almost got it.",NULL]:sorry:=[" Sorry, that's not right."," Nope, but don't give up."," Not quite, it's a little off."," Bummer, thought you would get it this time."," If you need help, please ask a human."," I don't know where you went wrong."," Sorry, killer problem."," No, but don't blow it off."," D'oh!"," That's whack."," Thought you would get it this time."," Nice try, but your answer is wrong."," Ask your neighbor for help."," Brutal kid."," That won't fly."," So close and yet so far."," So, that was just practice."," A swing and a miss."," Better luck next time."," Oops."," Tilt. Play again."," I know you can do better."," Sorry Charlie."," Tisk, tisk. It's a tough one."," It takes a lot of wrongs to make a right."," Even Einstein didn't get everything right."," Today's not your lucky day."," Don't quit your day job."," You're colder than a polar bear's toenail.",op(almost),NULL]:trygeneric:=[" Fix your answer and check it again."," Give it another try."," Try again."," Please try again.",NULL]:tryhint:=[" Try the hints and answer again."," Read the hints and try again."," Study the hints and answer again.",NULL]:tryhelp:=[" Try the Help menu and answer again."," Look at the Help menu and try again.",NULL]:showgeneric:=[" OK That's just practice. But try doing it yourself."," That's fine for practice. Try doing it yourself."," Think about it and enter an answer yourself."," Next time, compute an answer yourself."," So that was practice. Try doing it yourself.",NULL]:showhint:=[" Next time, try the hints."," Read the hints and enter an answer yourself.",NULL]:showhelp:=[" Next time, read the Help menu."," Read the Help and enter an answer yourself.",NULL]:# ################################### Procs for all maplets.GetVersion:=proc()local S, S1, S3, S4;options `Copyright 2009-10, Philip B. Yasskin and Douglas B. Meade, Maplets for Calculus`;uses StringTools;S:=interface(version);S:=map( Trim, Split( S, "," ) );S1:=Split(S[1], " " );S3:=Split(S[3], " " );S4:=Split(S[-1], " " );sprintf("%s (%s)", S[2],S3[-1]);end proc:#################################### # Customize For Each Mapletwith(LinearAlgebra):
with(plots):nextlocal:=[NULL]:trylocal:=[NULL]:showlocal:=[NULL]:nexts1:=[ #Keep what is appropriate. This is for all but the last check.op(nextgeneric),#op(nextprob),#op(nextquest),op(nextpart),op(nextstep),#op(nextlocal),NULL]:nexts2:=[ #Keep what is appropriate. This is for the last check.op(nextgeneric),op(nextprob),op(nextquest),op(nexteq),#op(nextfn),#op(nextlim),#op(nextderiv),#op(nextinteg),#op(nextdiffeq),#op(nextseq),#op(nextser),#op(nextlocal),NULL]:trys:=[ #Keep what is appropriate.op(trygeneric),#op(tryhint),op(tryhelp),#op(trylocal),NULL]:shows:=[ #Keep what is appropriate.op(showgeneric),#op(showhint),op(showhelp),#op(showlocal),NULL]:randgreat:=rand(1..nops(great)):randnext1:=rand(1..nops(nexts1)):randnext2:=rand(1..nops(nexts2)):randalmost:=rand(1..nops(almost)):randsorry:=rand(1..nops(sorry)):randtry:=rand(1..nops(trys)):randshow:=rand(1..nops(shows)):# ###################################### # English Translation Table for Line-Plane Intersection# Fill this out
TEXTLasstprogrammer:="Raquel Belnap & Farhan Siddiqui":
TEXTTitleMain:="Intersection of 2 Lines in R^3":
TEXTGoal:="Goal: Determine if the following lines are parallel, skew or intersecting. If intersecting, find the point of intersection.":
TEXTtheLineA:="the line A":
TEXTtheLineB:="and the line B":
TEXTFindvNvN:="Equations of x & y:":TEXTHint2:="Equate x & y components to solve for s & t.":
TEXTHint3:="Evaulate the line at these values of s & t.":
TEXTHint4:="Substitute the value of t that you found back into the line to find the point of intersection.":TEXTX:="X =":
TEXTY:="Y =":
TEXTS:="S =":
TEXTT:="T =":
TEXTRBPara:="Parallel":
TEXTPtInt:="Step 2:Evaluate the lines at these values of s & t :":
TEXTSubPlane:="Blahh:":
TEXTSolveT:="Solve for s:":
TEXT2:="Solve for t:":
TEXTSubT:="Solve for t:":
TEXTSkIn:="Step 3: Find if the lines are skew or intersecting:":
################### Maplet Code Startrand14:=rand(1..4):
randt0:=rand(-3..4):
comps:=[-2,-1,1,2]:
randrel:=rand(1..5):plotf:=proc()
global X1, X2;
local plotf1:=spacecurve(X1, t=-20+t0..20+t0, color=red, thickness=3, numpoints=2000):
local plotf2:=spacecurve(X2, s=-20+s0..20+s0, color=blue, thickness=3, numpoints=2000):
Set(myplot=display(plotf1,plotf2, axes=normal, view=[-10..10,-10..10,-10..10])):
end proc:funcgen:=proc()
global X1,X2,vec1,vec2,P0,P0z,P1,P2,s0,t0,whichrel, xeq, yeq,r1t,r2s:
local a:=comps[rand14()]:
local b:=comps[rand14()]:
local c:=comps[rand14()]:
local d:=comps[rand14()]:
local e:=comps[rand14()]:
local f:=comps[rand14()]:
local g:=comps[rand14()]:
local h:=comps[rand14()]:
local j:=comps[rand14()]:
local k:=comps[rand14()]:
while k=j do
k:=comps[rand14()]
end do:
vec1:=[a,b,c]:
vec2:=[d,e,f]:
P0:=[g,h,j]:
P0z:=[g,h,k]:
s0:=comps[rand14()];
t0:=comps[rand14()];
whichrel:=randrel();
P1:=P0-t0*vec1;
X1:=expand(P1+t*vec1);
if whichrel=1 then
P2:=P0-s0*vec2;
vec2:=vec1;
X2:=expand(P2+s*vec2);
elif whichrel in {2,3} then
P2:=P0-s0*vec2;
X2:=expand(P2+s*vec2);
elif whichrel in {4,5} then
P2:=P0z-s0*vec2;
X2:=expand(P2+s*vec2);
end if;
xeq:=X1[1]=X2[1]:
yeq:=X1[2]=X2[2]:
r1t:=expand(P1+t0*vec1);
r2s:=expand(P2+s0*vec2);
Set(TFr1=map(sort,X1,[t],ascending));
Set(TFr2=map(sort,X2,[s],ascending));
Set(reply="", reply(background)=white):
Set(TFv1=""):
Set(TFv2=""):
Set(RBpara=false):
Set(RBnotpara=false):
Set(replypara="", replypara(background)=white):
Set(TFxeq=""):
Set(TFyeq=""):
Set(replyeqs="", replyeqs(background)=white):
Set(TFtval=""):
Set(TFsval=""):
Set(replyts="", replyts(background)=white):
Set(TFr1t=""):
Set(TFr2s=""):
Set(replyinter="", replyinter(background)=white):
Set(myplot=display(plot3d(0,x=0..0, y=0..0))):
Set(BCkpara(enabled)=true):
Set(BShpara(enabled)=true):
Set(BCkeqs(enabled)=false):
Set(BSheqs(enabled)=false):
Set(BCkts(enabled)=false):
Set(BShts(enabled)=false):
Set(BCkinter(enabled)=false):
Set(BShinter(enabled)=false):
Set(RBinter=false):
Set(RBskew=false):
end proc:hintpara:=proc()
Set(reply="The tangent to each line is the vector of coefficients of t or s in the parametric equations of the line. The lines are parallel if one tangent is a scalar multiple of the other.",
reply(background)=ColorHint, reply(foreground)=ColorHintFrgd):
end proc:ispara:=proc(v1,v2)
is(v1[1]*v2[2]=v2[1]*v1[2] and v1[3]*v2[2]=v2[3]*v1[2]);
end proc:checkpara:=proc()
global vec1,vec2:
local userv1, userv2, message, correct, para:
if Get(TFv1)="" or Get(TFv2)="" or not (Get(RBpara) or Get(RBnotpara)) then
Set(replypara="",
replypara(background)=ColorMessage):
Set(reply=sprintf(TEXTreplyNoChecks,3),
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd):
return:
end if:
userv1:=Get(TFv1::list, corrections=true, update=true):
userv2:=Get(TFv2::list, corrections=true, update=true):
correct:=true;
if ispara(userv1,vec1) then
message:="v1 is correct. ";
else
message:="v1 is incorrect. ";
correct:=false;
end if:
if ispara(userv2,vec2) then
message:=cat(message, "v2 is correct. ");
else
message:=cat(message, "v2 is incorrect. ");
correct:=false;
end if:
if not correct then
Set(replypara=TEXTIncorrect,
replypara(background)=ColorIncorrect, replypara(foreground)=ColorIncorrectFrgd):
Set(reply=cat(message,
"You must get both vectors correct before I will tell you if the rest is correct."),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
return;
end if;
para:=ispara(vec1,vec2);
if ( para and Get(RBpara) ) or ( not para and Get(RBnotpara) ) then
Set(replypara=TEXTCorrect,
replypara(background)=ColorCorrect, replypara(foreground)=ColorCorrectFrgd):
if para then
Set(reply=cat(great[randgreat()], "Since they are parallel, there is no point of intersection.", nexts2[randnext2()]),
reply(background)=green, reply(foreground)=ColorCorrectFrgd):
plotf():
else
Set(reply=cat(great[randgreat()], "Since they are not parallel, find the point of intersection or determine if they are skew.",nexts1[randnext1()]),
reply(background)=green, reply(foreground)=ColorCorrectFrgd,
BCkeqs(enabled)=true, BSheqs(enabled)=true):
end if
else
Set(replypara=TEXTIncorrect,
replypara(background)=ColorIncorrect, replypara(foreground)=ColorIncorrectFrgd):
Set(reply=cat(message,"The lines are parallel if their tangents are proportional. Try again."),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
return;
end if:
end proc:showpara:=proc()
global X1,X2,vec1,vec2,P0,P0z,P1,P2,s0,t0,whichrel:
Set(TFv1=vec1):
Set(TFv2=vec2):
if vec1=vec2 then
Set(RBpara=true):
plotf():
else
Set(RBnotpara=true):
Set(BCkeqs(enabled)=true, BSheqs(enabled)=true);
end if:
Set(replypara=TEXTShown,
replypara(background)=ColorShow, replypara(foreground)=ColorCorrectFrgd):
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd):
end proc:hinteqs:=proc()
Set(reply="Equate x and y components. Solving these will tell you where the lines have the same x and y components but not necessarily z components.",
reply(background)=ColorHint, reply(foreground)=ColorHintFrgd):
end proc:checkeqs:=proc()
global xeq, yeq:
local userxeq, useryeq, correct, message:
if Get(TFxeq)=""or Get(TFyeq)="" then
Set(replyeqs="",
replyeqs(background)=ColorMessage):
Set(reply="Enter Answers.",
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd):
return:
end if:
userxeq:=Get(TFxeq::equation, corrections=true, update=true):
useryeq:=Get(TFyeq::equation, corrections=true, update=true):
correct:=true;
if lhs(userxeq)<>lhs(xeq) or rhs(userxeq)<>rhs(xeq) then
message:=" Equation x is incorrect.";
correct:=false;
else
message:=" Equation x is correct.";
end if:
if lhs(useryeq)<>lhs(yeq) or rhs(useryeq)<>rhs(yeq) then
message:=cat(message," Equation y is incorrect.");
correct:=false;
else
message:=cat(message," Equation y is correct.");
end if:
if correct then
Set(replyeqs=TEXTCorrect,
replyeqs(background)=ColorCorrect, replyeqs(foreground)=ColorCorrectFrgd):
Set(reply=cat(great[randgreat()], nexts1[randnext1()]),
reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd):
Set(BCkts(enabled)=true):
Set(BShts(enabled)=true):
else
Set(replyeqs=TEXTIncorrect,
replyeqs(background)=ColorIncorrect, replyeqs(foreground)=ColorIncorrectFrgd):
Set(reply=cat(message,
" Fix your answer and check again."),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
end if;
end proc:showeqs:=proc()
global xeq,yeq:
Set(TFxeq=xeq):
Set(TFyeq=yeq):
Set(replyeqs=TEXTShown,
replyeqs(background)=ColorShow, replyeqs(foreground)=ColorCorrectFrgd):
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd):
Set(BCkts(enabled)=true):
Set(BShts(enabled)=true):
end proc:hintts:=proc()
Set(reply="Solve one equation for t or s and plug into the other equation.",
reply(background)=ColorHint, reply(foreground)=ColorHintFrgd):
end proc:checkts:=proc()
local usert, users:
if Get(TFtval)=""or Get(TFsval)="" then
Set(replyts="",
replyts(background)=ColorMessage):
Set(reply=TEXTreplyNoCheck,
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd):
return:
end if:
usert:=Get(TFtval::algebraic, corrections=true, update=true):
users:=Get(TFsval::algebraic, corrections=true, update=true):
if usert=t0 and users=s0 then
Set(replyts=TEXTCorrect,
replyts(background)=green, replyts(foreground)=ColorCorrectFrgd):
Set(reply=cat(great[randgreat()], nexts1[randnext1()]),
reply(background)=green, reply(foreground)=ColorCorrectFrgd):
Set(BCkinter(enabled)=true):
Set(BShinter(enabled)=true):
else
Set(replyts=TEXTIncorrect,
replyts(background)=ColorIncorrect, replyts(foreground)=ColorIncorrectFrgd):
Set(reply=cat(sorry[randsorry()], trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
end if:
end proc:showts:=proc()
Set(TFtval=t0):
Set(TFsval=s0):
Set(replyts=TEXTShown,
replyts(background)=ColorShow, replyts(foreground)=ColorCorrectFrgd):
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd):
Set(BCkinter(enabled)=true):
Set(BShinter(enabled)=true):
end proc:hintinter:=proc()
Set(reply="Substitute the value of t into r1(t) and the value of s into r2(s). If these are the same, then this is the point of intersection. Otherwise they are skew.",
reply(background)=ColorHint, reply(foreground)=ColorHintFrgd):
end proc:checkinter:=proc()
global r1t, r2s:
local user1, user2,correct, inter,message:
if Get(TFr1t)="" or Get(TFr2s)="" or not (Get(RBinter) or Get(RBskew)) then
print(a=Get(TFr1t),b=Get(TFr2s),c=Get(RBinter),d=Get(RBskew));
Set(replyinter="",
replyinter(background)=ColorMessage):
Set(reply=sprintf(TEXTreplyNoChecks,3),
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd):
return:
end if:
user1:=Get(TFr1t::list, corrections=true, update=true):
user2:=Get(TFr2s::list, corrections=true, update=true):
correct:=true;
if user1<>r1t then
message:="r1(t) is incorrect.":
correct:=false:
else
message:="r1(t) is correct.":
end if:
if user2<>r2s then
message:=cat(message,"r2(s) is incorrect."):
correct:=false:
else
message:=cat(message, "r2(s) is correct."):
end if:
if not correct then
Set(replyinter=TEXTIncorrect,
replyinter(background)=ColorIncorrect, replyinter(foreground)=ColorIncorrectFrgd):
Set(reply=cat(message, "You must get these both correct before I will tell you if the rest is correct."),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
return:
end if:
if r1t=r2s then
inter:=true:
else
inter:=false:
end if:
if ( inter and Get(RBinter) ) or ( not inter and Get(RBskew) ) then
Set(replyinter=TEXTCorrect, replyinter(background)=ColorCorrect, replyinter(foreground)=ColorCorrectFrgd):
if inter then
Set(reply=cat(great[randgreat()], "They are intersecting. Good job!", nexts2[randnext2()]),
reply(background)=green, reply(foreground)=ColorCorrectFrgd):
else
Set(reply=cat(great[randgreat()], "They are skew. Good job!",nexts2[randnext2()]),
reply(background)=green, reply(foreground)=ColorCorrectFrgd):
end if:
plotf():
else
Set(replyinter=TEXTIncorrect,
replyinter(background)=ColorIncorrect, replyinter(foreground)=ColorIncorrectFrgd):
Set(reply=cat(message,"The lines are parallel if their tangents are proportional. Try again."),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
end if:
end proc:showinter:=proc()
global r1t,r2s:
Set(TFr1t=r1t):
Set(TFr2s=r2s):
if r1t=r2s then
Set(RBinter=true):
else
Set(RBskew=true):
end if:
Set(replyinter=TEXTShown,
replyinter(background)=ColorShow, replyinter(foreground)=ColorCorrectFrgd):
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd):
plotf():
end proc:LineRelationship:=Maplet(onstartup = RunWindow(MAIN),
Window[MAIN](title=TEXTTitleMain,
[ valign=none, inset=0, spacing=0,
[ halign=none,
Button(TEXTBNewFunction, Evaluate(function="funcgen"), background=ColorNewButton),
HorizontalGlue(),
BoxRow( halign=none, border=true,
caption=TEXTGoal,
HorizontalGlue(),
"Line r1(t) =",
TextField[TFr1](width=20, editable=false, background=white),
HorizontalGlue(),
"Line r2(s) =",
TextField[TFr2](width=20, editable=false, background=white),
HorizontalGlue()
),
HorizontalGlue(),
Button(TEXTBQuit, Shutdown(), background=pink)
],
[ halign=none, inset=0, spacing=0,
[ border=true, caption=TEXTBPlot,
[ background=gold, Plotter[myplot](width=250,height=250)
]
],
[ valign=none, inset=0, spacing=0,
BoxColumn( valign=none, inset=0, spacing=0, border=true,
caption="Step 1: Determine if the lines are parallel:",
[ halign=none,
"Find the tangent vectors: v1 =",
TextField[TFv1](width=7),
" v2 =",
TextField[TFv2](width=7),
HorizontalGlue()
],
[ halign=none,
"Select:",
HorizontalGlue(),
RadioButton[RBpara]("Parallel", group=BGpara),
HorizontalGlue(),
RadioButton[RBnotpara]("Not Parallel", group=BGpara),
HorizontalGlue(),
Button[BHtpara](TEXTBHint, Evaluate(function="hintpara"), background=ColorHintButton),
Button[BCkpara](TEXTBCheck, Evaluate(function="checkpara"), background=ColorCheckButton, enabled=false),
TextField[replypara](width=7, editable=false, background=white),
Button[BShpara](TEXTBShow, Evaluate(function="showpara"), background=ColorShowButton, enabled=false)
]
),
BoxColumn( valign=none, inset=0, spacing=0, border=true,
caption="Step 2: Equate the x & y components and solve for t & s:",
[ halign=none,
"x Equation:",
TextField[TFxeq](width=11),
HorizontalGlue(),
"y Equation:",
TextField[TFyeq](width=11),
HorizontalGlue(),
Button[BHteqs](TEXTBHint, Evaluate(function="hinteqs"), background=ColorHintButton),
Button[BCkeqs](TEXTBCheck, Evaluate(function="checkeqs"), background=ColorCheckButton, enabled=false),
TextField[replyeqs](width=7, editable=false, background=white),
Button[BSheqs](TEXTBShow, Evaluate(function="showeqs"), background=ColorShowButton, enabled=false)
],
[ halign=none,
"t =",
TextField[TFtval](width=10),
HorizontalGlue(),
"s =",
TextField[TFsval](width=10),
HorizontalGlue(),
Button[BHtts](TEXTBHint, Evaluate(function="hintts"), background=ColorHintButton),
Button[BCkts](TEXTBCheck, Evaluate(function="checkts"), background=ColorCheckButton, enabled=false),
TextField[replyts](width=7, editable=false, background=white),
Button[BShts](TEXTBShow, Evaluate(function="showts"), background=ColorShowButton, enabled=false)
]
),
BoxColumn( valign=none, inset=0, spacing=0, border=true,
caption="Step 3: Evaluate the lines at these values of t & s:",
[ halign=none,
"r1(t) =",
TextField[TFr1t](width=10),
" r2(s) =",
TextField[TFr2s](width=10),
HorizontalGlue()
],
[ halign=none,
"Select:",
HorizontalGlue(),
RadioButton[RBskew]("Skew", group=BGinter),
HorizontalGlue(),
RadioButton[RBinter]("Intersecting", group=BGinter),
HorizontalGlue(),
Button[BHtinter](TEXTBHint, Evaluate(function="hintinter"), background=ColorHintButton),
Button[BCkinter](TEXTBCheck, Evaluate(function="checkinter"), background=ColorCheckButton, enabled=false),
TextField[replyinter](width=7, editable=false, background=white),
Button[BShinter](TEXTBShow, Evaluate(function="showinter"), background=ColorShowButton, enabled=false)
]
)
]
],
[ TextBox[reply](width=85, height=3, editable=false, background=white)
],
BoxColumn( halign=none, background=ColorFooter, inset=0, spacing=0,
[ background=ColorFooter, inset=0, spacing=0,
Label(TEXTLprogrammers, font=FontFooter),
" ", HorizontalGlue(),
Label(TEXTLcopyright, font=FontFooter),
" ", HorizontalGlue(),
Label(TEXTLversion, font=FontFooter)
],
[ background=ColorFooter, inset=0, spacing=0,
Label(TEXTLasstprogrammer, font=FontFooter),
HorizontalGlue(),
Label(GetVersion(), font=FontFooter)
]
)
]
),
ButtonGroup[BGpara](),
ButtonGroup[BGinter]()
): Maplets[Display]( LineRelationship );