Question

If the vectors a and b are mutually perpendicular, then $\mathbf{a} \times \{\mathbf{a} \times \{\mathbf{a} \times (\mathbf{a} \times \mathbf{b})\}\}$ is equal to

• A. $|\mathbf{a}|^{2}\mathbf{b}$
• B. $|\mathbf{a}|^{3}\mathbf{b}$
• C. $|\mathbf{a}|^{4}\mathbf{b}$
• D. None of these

Answer 1

Answer: (C)

$|\mathbf{a}|^{4}\mathbf{b}$

Answer 2

$\mathbf{a} \times \lbrack\mathbf{a} \times \{\mathbf{a} \times (\mathbf{a} \times \mathbf{b})\}\rbrack = \mathbf{a} \times \lbrack\mathbf{a} \times \{\mathbf{a} \times ab\widehat{\mathbf{n}}\}\rbrack$

$= \mathbf{a} \times \lbrack\mathbf{a} \times a^{2}\mathbf{b}\rbrack = \mathbf{a} \times a^{3}b\widehat{\mathbf{n}} = |\mathbf{a}|^{4}\mathbf{b}.$