Question

Relative to an origin O, the position vectors of points A and B are given by
OA = 3pi + 4j + p^2k, and
OB = -pi + -1j + p^2k

Find the values of p for which angle AOB is 90°

So here's my work so far:
If angle = 90° then OA.OB = 0
OA.OB = p^4 - 3p^2 - 4
p^4 - 3p^2 - 4 = 0

Let x = p^2
x^2 - 3x - 4 = 0
x = 4 or -1

What do I do now?

Thanks for the help!

Answer 1

remember you let y = p^2
so p^2 = 4 ----> p = ± 2
or
p^2 = -1 , which has no real solution.

so p = ± 2

Answer 2

Wait, but doesn't the question say 'values'?

Answer 3

Oh wait, just realized how dumb that was! Had a brain fart, thanks for clearing things up!