Question

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

Answer 1

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>