Physics, asked by sahastomar918, 9 months ago

The resultant of two vectors P and Q is equal to R. On reversing the
direction of Q ,the resultant becomes S.
Prove that R2 + S2 = 2 ( P2+Q2
)

Answers

Answered by LoverLoser
22

Given-

  • P + Q = R

On reversing,

  • - R = - P - Q
  • S = - P - Q

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vectors in question follow the triangle law of vectors.

\boxed{R^2= P^2 + Q^2 + 2 PQ cos \theta}----(1)

So,

S^2 = P^2 + (-Q^2)+ 2P (-Q) cos \theta---(2)

On adding (1) and (2) we get

so,

R^2 + S^2 = (P^2+Q^2) + (P^2+Q^2)

R^2 + S^2 =2\times  (P^2+Q^2)

Hence Proved!

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