The value of
\( \vec{a} \times (\vec{b} \times \vec{c}) \)
is:
Show Hint
- $(\vec{a} \cdot \vec{c})\vec{b} - (\vec{a} \cdot \vec{b})\vec{c}$
- $(\vec{a} \cdot \vec{b})\vec{c} - (\vec{a} \cdot \vec{c})\vec{b}$
- $(\vec{b} \cdot \vec{c})\vec{a} - (\vec{a} \cdot \vec{b})\vec{c}$
- None of these
The Correct Option is A
Solution and Explanation
This is the standard formula for the Vector Triple Product.
Step 2: Analysis
The vector triple product $\vec{a} \times (\vec{b} \times \vec{c})$ results in a vector that lies in the plane of $\vec{b}$ and $\vec{c}$.
Step 3: Conclusion
The expansion is $(\vec{a} \cdot \vec{c})\vec{b} - (\vec{a} \cdot \vec{b})\vec{c}$.
Final Answer: (A)
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