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  • The resultant vector P and Q is R.on reversing the direction of the angle the resultant becomes S.show that R sq.+S sq.=2(P sq.+Q sq.)

The resultant vector P and Q is R.on reversing the direction of the angle the resultant becomes S.show that R sq.+S sq.=2(P sq.+Q sq.)

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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)
 

Posted by

avinash.dongre

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