Question

Find all values of
b
for which the vectors

5, −4, 4

and

b2, b, 0

are orthogonal. (Enter your answers as a comma-separated list.)

Answer 1

The vectors will be orthogonal if their dot product is zero.

$\langle5,-4,4\rangle\cdot\left\langle b^2,b,0\right\rangle=5b^2-4b=0$

You have

$5b^2-4b=b(5b-4)=0\implies b=0,b=\dfrac45$