For any vector a prove that |a i|^2+|a j|^2+|a k|^2=2|a|^2 - Vidyadip

Question

For any vector $\vec{a}$ prove that $|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2=2|a|^2$

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