Name: Bryan Murray

Account Name: btm6580

Attendance Sheet #: NA

Assignment #: 1

Problem #: 1.2.16

URL: http://acs.tamu.edu/~btm658b/m311p1_2_161.html


Characterize the line [Maple Math] by a pair of equations, [Maple Math] and [Maple Math] . (Find two distinct planes containing the line. There are many different correct answers!)


The line, [Maple Math] , can simply be treated as the vector [Maple Math] . First, two vectors must be found which are orthogonal to [Maple Math] , these will be the vectors [Maple Math] and [Maple Math] . To find these vectors one picks the first two components of the vectors and then calculates the third so that the dot product of [Maple Math] and [Maple Math] and [Maple Math] and [Maple Math] is equal to 0. To find the first vector I simply chose -1 and 2 to be the first two components and then calculated the third component to be -1, ending up with [Maple Math] . By the same process [Maple Math] , was found. Therefore the line is characterized by the pair of equations [Maple Math] and [Maple Math] . Also, since orthogonal vectors make up the coefficients in the standard form of a plane, the line can be characterized by the equations [Maple Math] and [Maple Math] .