If u=<-7,6> and v=<-4,17>, which vector can be added to u+3v to getthe unit vector <1,0> as the resultant vector?

Question

Answer Choices

A. W=<18,-57>

B. W=<18,-45>

C. W=<20,-57>

D. W=<20,-45>

Answer 1

u = <-7, 6>

v = <-4, 17>

3v = <3(-4), 3(17)> = <-12, 51>

u + 3v = <-7-12, 6+51> = <-19, 57>

Let w = <x, y>

We want u + 3v + w = <1, 0>

<-19+x, 57+y> = <1, 0>

So:

-19+x = 1

57+y = 0

Solve for x and y to get w.