Question

If vector P+vector Q=vector R ;and if P^2+Q^2=R^2 then find the angle between the vectorP and vectorQ?

Answer 1

`bbP, bbQ` are orthogonal.

(This should be clear from the start - Pythagoreas' Theorem)

Explanation:

`bbP + bbQ = bbR`

• `(bbP + bbQ)*(bbP + bbQ)`

`= P^2 + Q^2 + 2 bbP*bbQ`

`= R^2 + 2 bbP*bbQqquad square`

And because `(bbP + bbQ) = bbR`

• `(bbP + bbQ) * (bbP + bbQ) = bbR * bbR = R^2 qquad triangle`

`square = triangle implies bbP*bbQ = 0`

`bbP*bbQ = abs bbP abs bbQ cos alpha implies color(red)(alpha = pm pi/2)`