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

1 Answer
Jun 15, 2018

#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)#