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$\mathbf{a}=\mathbf{i}+\mathbf{j}-2 \mathbf{k} \Rightarrow \sum\{(\mathbf{a} \times \mathbf{i}) \times \mathbf{j}\}^2$ is equal to
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The correct answer is:
$6$
Given, $\mathbf{a}=\mathbf{i}+\mathbf{j}-2 \mathbf{k}$
$\begin{aligned} \therefore \quad & \sum[(\mathbf{a} \times \mathbf{i}) \times \mathbf{j}]^2=\sum[(\mathbf{a} \cdot \mathbf{j}) \mathbf{i}]^2 \\ & =\mathbf{a}^2=|\mathbf{i}+\mathbf{j}-2 \mathbf{k}|^2 \\ & =(\sqrt{1+1+4})^2=6\end{aligned}$
$\begin{aligned} \therefore \quad & \sum[(\mathbf{a} \times \mathbf{i}) \times \mathbf{j}]^2=\sum[(\mathbf{a} \cdot \mathbf{j}) \mathbf{i}]^2 \\ & =\mathbf{a}^2=|\mathbf{i}+\mathbf{j}-2 \mathbf{k}|^2 \\ & =(\sqrt{1+1+4})^2=6\end{aligned}$
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