Question

For vectors u=-6i +2k and v=7i-4j, find (-3u)*v.

A) -450
B) -50
C) 108
D) 150

I know how to do these problems, but I am stuck on this question, because I keep finding the answer 118. I know you change -6i+2j to (-6,2) and 7i-4j to (7,-4) and then plug them into the equation but I don't know what I am doing wrong.

Answer 1

You can compute the dot product in the usual way, then multiply the result by -3, or you can multiply u by -3, then compute the dot product. Either way, it is 150.

-3(u•v) = -3*((-6)*7 +2*(-4)) = -3*(-42 -8) = -3*(-50) = 150

(-3u)•v = (18i -6j)•(7i -4j) = 18*7 +(-6)(-4) = 126 +24 = 150


Selection D is appropriate.