Question

find the value of b such that u=(-2,4,2) ¡ì v=(b,b^2,1) are orthogonals.

Answer 1

to be orthogonal, the dot product must be zero

-2b + 4b^2 + 2 = 0
2b^2 - b + 1 = 0

b = (1 ± √-7)/4

No real value of b will make your two given vectors orthogonal