Prove that for any two vectors

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Prove that for any two vectors a,b∈R3\mathbf a,\mathbf b\in\mathbb R^{3}, the following identity holds: ∣a+b∣2=∣a∣2+∣b∣2+2 a⋅b.|\mathbf a+\mathbf b|^{2}=|\mathbf a|^{2}+|\mathbf b|^{2}+2\,\mathbf a\cdot\mathbf b.

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