Question

If $\mathbf{a} = \mathbf{i} + 2\mathbf{j} - 2\mathbf{k},\mathbf{b} = 2\mathbf{i} - \mathbf{j} + \mathbf{k}$and $\mathbf{c} = \mathbf{i} + 3\mathbf{j} - \mathbf{k},$

then $\mathbf{a} \times (\mathbf{b} \times \mathbf{c})$ is equal to

• A. $20\mathbf{i} - 3\mathbf{j} + 7\mathbf{k}$
• B. $20\mathbf{i} - 3\mathbf{j} - 7\mathbf{k}$
• C. $20\mathbf{i} + 3\mathbf{j} - 7\mathbf{k}$
• D. None of these

Answer 1

Answer: (A)

$20\mathbf{i} - 3\mathbf{j} + 7\mathbf{k}$

Answer 2

$\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \mathbf{a} \times \left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2 & - 1 & 1 \\ 1 & 3 & - 1 \end{matrix} \right| = \mathbf{a} \times ( - 2\mathbf{i} + 3\mathbf{j} + 7\mathbf{k})$

\mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 2 & - 2 \\ - 2 & 3 & 7 \end{matrix} \right| = 20\mathbf{i} - 3\mathbf{j} + 7\mathbf{k}.$$