Math - Vectors

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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!

  • Math - Vectors -

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

    so p = ± 2

  • Math - Vectors -

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

  • Math - Vectors -

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

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