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If vecP+vecQ=vecR and vecP-vecQ=vecS, pr...

If `vecP+vecQ=vecR` and `vecP-vecQ=vecS`, prove that `vecR^2+vecS^2=2(vecP^2+vecQ^2)`

Text Solution

Verified by Experts

Let angle between `vecP and vecQ` be `theta`
`vecP+vecQ=vecR rArr P^(2)+Q^(2)+2PQ cos theta =R^(2)`
`vecP-vecQ=vecSrArr P^(2)+Q^(2)-2PQ cos theta =s^(2)`
On adding equations (i) and (ii) we get
`2(P^(2)+Q^(2))=R^(2)+S^(2)`
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