For what values of b are the vectors [-6, b, 2] and [b, b2, b] orthognal

b = 2, 0, - 2

Step-by-step explanation:

This is a multivariable calculus question and two vectors are orthogonal if and only if their dot product is zero. Since

[-6, b, 2]. [b, b², b] = - 6b + b³ + 2b

= - 4b + b³

=b (4+b²)

= = b (2²+b²)

==b (b-2) (b+2)

The given vectors are orthogonal if b = - 2,

b = 0,

b = 2