David Logsdon d-logsdon
Assignment 1
1.1.4
We are given the following vectors in a previous problem:
> x:= vector(3,[1,2,3]); y:= vector(3,[1,-1,1]); z:= vector(3,[-2,2,-2]);
As requested we compute the dot products of the vector x with the vectors y and z.
> dotprod(x,y);
> dotprod(x,z);
We note that the vectors y and z are scalar multiples of each other.
That is to say that y=.5z and z=
-2y.
Thus we have the following two sets of equations:
[1] x*z= -4 z= -2y
and
[2] x*y=
2 y= -.5z
Solving [1] gives:
x*(-2)y = -4
which simplifies to:
x*y = 2
Solving [2] gives:
x*(-.5)z= 2
which simplifies to:
x*z = -4
We can generalize these results to arrive at the following conclusion
for any scalar c, vectors
X1 and X2, and some real number
n:
If X1*X2 = n
Then (cX1*X2)= (X1*cX2) = c(X1*X2) = cn