For what values of b are the vectors [−18, b, 9] and [b, b2, b] orthogonal? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) b =

Therefore the given vectors are orthogonal for b = 0,±3.

Step-by-step explanation:

If   and   are two vectors orthogonal, then the dot product of and will be zero.

i.e

If    and

Given two vectors are (-18,b,9) and (b,b²,b)

Let

and

Therefore,

=(-18).b+b.b²+9.b

= -18b+b³+9b

= b³-9b

Since and are orthogonal. Then = 0.

Therefore,

b³-9b= 0

⇒b(b²-9)=0

⇒b =0 or b²=9

⇒b=0 or b =±3

Therefore the given vectors are orthogonal for b = 0,±3.

the correct answer is 828.07