Question

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

Answer 1

Answer:

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