Find all constants a such that the vectors (a, 2) and (a, −2) are orthogonal.

Question

Find all constants a such that the vectors (a, 2) and (a, −2) are orthogonal.

Answer 1

If <a,2> and <a,-2> are orthogonal, then the dot product of the two vectors must be zero.

<a, 2> • <a, -2> = 0

So, a² - 4 = 0

a² = 4

a = 2 or -2