Find the value of k so that the vectors u and v are orthogonal.

Question

u = 30i + 6j

v = 5i - kj

k = ______

Answer 1

u = 30i + 6j

v = 5i - kj

u . v = Ιl u ll ll v ll cos θ

If two vectors orthogonal , θ = π/2

u . v = Ιl u ll ll v ll cos π/2

cos π/2 = 0

u . v = 0

0 = 30* 5 - 6*k

6k = 150

k = 150/6 = 25

Answer 2

(30)(5) + (6)(-k) = 0