Wednesday, December 9, 2009

P,Q,R,S are four vectors of equal magnitude. P + Q - R = 0, where the angle between P and Q is P + Q - S = 0, where the angle between...

Hello!


First, rewrite the equalities as P + Q = R and P + Q = S. We see now that R = S, so is the angle between P and Q, is the angle between P and P + Q.


P + Q is the diagonal of the parallelogram formed by P and Q. Because P and Q have the equal magnitudes, this parallelogram is a rhombus, and its diagonals bisect the angles between the sides.


Thus is a half of , and the ratio is : is 2 : 1.


If we take into account that the magnitude of P+Q is the same of P and Q, we find that and

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