The resultant of two forces P and Q is R. If one of the forces is reversed in direction, then the resultant becomes S. Then for the identity R² + S² = 2(P² + Q²) to hold goo
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The vectors follow the triangle law of vectors.
So $R^{2}=P^{2}+Q^{2}+2PQ \cos \theta $
On reversing the direction of Q we get -Q
So
$S^{2}=P^{2}+(-Q)^{2}+2 P(-Q) \cos \theta
The last third terms get canceled out on adding
So
$R^{2}+S^{2}=\left(P^{2}+Q^{2}\right)+\left(P^{2}+Q^{2}\right)$\\ \Rightarrow R^{2}+S^{2}=2*\left(P^{2}+Q^{2}\right)
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