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Question: Answered & Verified by Expert
If the vectors $\mathbf{a}$ and $\mathbf{b}$ are mutually perpendicular, then $\mathbf{a} \times\{\mathbf{a} \times\{\mathbf{a} \times(\mathbf{a} \times \mathbf{b})\}\}$ is equal to
MathematicsVector AlgebraJEE Main
Options:
  • A $|\mathbf{a}|^2 \mathbf{b}$
  • B $|\mathbf{a}|^3 \mathbf{b}$
  • C $|\mathbf{a}|^4 \mathbf{b}$
  • D None of these
Solution:
1235 Upvotes Verified Answer
The correct answer is: $|\mathbf{a}|^4 \mathbf{b}$
$\quad \mathbf{a} \times[\mathbf{a} \times\{\mathbf{a} \times(\mathbf{a} \times \mathbf{b})\}]=\mathbf{a} \times[\mathbf{a} \times\{\mathbf{a} \times \mathbf{a b} \hat{\mathbf{n}}\}]$
$=\mathbf{a} \times\left[\mathbf{a} \times a^2 \mathbf{b}\right]=\mathbf{a} \times a^3 b \hat{\mathbf{n}}=|\mathbf{a}|^4 \mathbf{b}$.

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