Question

Let u = <3, -1>, v = <-6, -6>. Find 9u + 2v.

Answer 1

<15,-21>

Explanation:

9u-2v

If u=<3,-1> then we multiply, 9.

v=<-6,-6>, so multiply it by 2.

9<3,-1> + 2<-6,-6>

Then, add the two together.

<27,-9> + <-12, -12>

= <15,-21>

Answer 2

9u means you're multiplying 9 into that vector, both components. Same with the 2v. 9*3 = 27 and 9*-1 = -9, so your new vector u is <27, -9>. Now let's do v. 2* -6 (twice) = -12, so your new v vector is <-12, -12>. Add those together now, first components of each and second components of each. 27 + (-12) = 15; -9+(-12)=-21. So the addition of those gives us a final vector with a displacement of <15, -21>