For what values of b are the vectors [−9, b, 5] and [b, b2, b] orthogonal? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) b

The values of b are [-2,0,2] for which the vectors are orthogonal.

Step-by-step explanation:

Given:

Vector [-9,b,5] and Vector [b,b^2,b].

According to the question:

Both the above vectors are orthogonal we have to find the value of b.

Orthogonal vectors:

So we have to calculate by dot product and make it equal to zero and then have to solve the b values.

Dot Product:

For vectors a and b where and the dot product is .

Solving.

⇒

⇒

⇒

⇒  ...taking b as common.

⇒

⇒ ...using algebraic identity,  .

⇒ Equating with zero individually.

⇒

So the values of b are [-2,0,2] for which the given vectors are orthogonal.