Question

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

Answer 1

b = 2, 0, -2

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