Question

If \(\vec c\) and \[ (\vec b\times \vec c)\times(\vec c\times \vec a) \] are parallel vectors, then \[ \left[\vec c\times\vec a\;\;\; \vec a\times\vec b\;\;\; \vec b\times\vec c\right] = \]

• A. \(0\)
• B. \(|\vec c|\)
• C. \[ \left( \frac{\left|(\vec b\times\vec c)\times(\vec c\times\vec a)\right|} {|\vec c|} \right)^2 \]
• D. \[ \left( \frac{|\vec b\times\vec c|} {|\vec c\times\vec a|} \right)^2 \]

Hint:

Remember the important identity \( [\vec a\times\vec b,\vec b\times\vec c,\vec c\times\vec a] = [\vec a,\vec b,\vec c]^2 \). It frequently appears in advanced vector algebra MCQs.

Answer 1

The Correct Option is C