If and , prove that…

MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors

Problem

If p+q=r\mathbf p+\mathbf q=\mathbf r and p−q=s\mathbf p-\mathbf q=\mathbf s, prove that ∥r∥2+∥s∥2=2(∥p∥2+∥q∥2)\lVert\mathbf r\rVert^2+\lVert\mathbf s\rVert^2=2\left(\lVert\mathbf p\rVert^2+\lVert\mathbf q\rVert^2\right).

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