Question

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​

Answer 1

Answer:

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)