Question

If \( \vec{a} \) and \( \vec{b} \) are two unit vectors, then the vector \[ (\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b}) \] is parallel to the vector

• A. \( \vec{a} + \vec{b} \)
• B. \( 2 \vec{a} + \vec{b} \)
• C. \( \vec{a} - \vec{b} \)
• D. \( 2 \vec{a} - \vec{b} \)

Hint:

Use the vector triple product identity \( \vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c} \) to simplify complex vector cross products.

Answer 1

The Correct Option is C

Step 1: Using vector triple product identity.
The expression \( (\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b}) \) simplifies using the vector triple product identity, resulting in a vector that is parallel to \( \vec{a} - \vec{b} \).

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } \vec{a} - \vec{b}} \]