Question

For which value(s) of k will the dot product of the vectors (k,2k-1, 3) and (k,5,-4) be 7?

I did this so far,

2k-1=5
6/2

k=3

Answer 1

what's the problem?

(k,2k-1,3)•(k,5,-4) = k*k + (2k-1)(5) + 3(-4)

so, we need

k^2 + 10k - 5 - 12 = 7
k^2 + 10k - 24 = 0
(k-2)(k+12) = 0
so, k=2 or -12

k=2: (2,3,3)•(2,5,-4) = 4+15-12 = 7
k=-12: (-12,-25,3)•(-12,5,-4) = 144-125-12 = 7