Question

For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated list.)

(−4, b, 3), (b, b^2, b)

Answer 1

(-4,b,3) ; (b,b²,b)

Dot product of Orthogonal is equal to zero.

(-4*b) + (b*b²) + (3*b) = 0
-4b + b³ + 3b = 0
b³ - b = 0

b can only have the value of 1 for the given vectors to be orthogonal.

b = 1

1³ - 1 = 0
1 - 1 = 0
0 = 0