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]);

x := vector([1, 2, 3])

y := vector([1, -1, 1])

z := vector([-2, 2, -2])

As requested we compute the dot products of the vector x with the vectors y and z.

> dotprod(x,y);

2

> dotprod(x,z);

-4

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