If vectors u and v are orthogonal and u=⟨2,−6⟩, find x if v=⟨x,−4⟩.

Question

How do I go about doing this and what is the answer?

Answer 1

For two vectors to be orthogonal, the dot product of the vectors must be zero

u • v = <2, -6> • < x, -4 > = 0

So, 2x + (-6)(-4) = 0

2x + 24 = 0

x = -12