Question

Determine the value of c so that for all real x, the vectors c xi – 6j – 3k and xi + 2j + 2c xk make an obtuse angle with each other.

Answer 1

Let a = c xi – 6j – 3k and b = x i + 2j + 2c xk 

Given, a.b < 0

c < 0 and c (3c + 4) < 0 

c < 0 and – (4/3) < c < 0

Hence, the value of c = (– (4/3), 0)