Question

Let \( \vec{a} = -\hat{i} + \hat{j} + 2\hat{k} \), \( \vec{b} = \hat{i} - \hat{j} - 3\hat{k} \), \( \vec{c} = \vec{a} \times \vec{b} \) and \( \vec{d} = \vec{c} \times \vec{a} \). Then \( (|\vec{a}|^2 - |\vec{b}|^2) \cdot \vec{d \) is equal to:}

• A. -4
• B. 4
• C. -2
• D. 2

Hint:

The vector \( \vec{d} = (\vec{a} \times \vec{b}) \times \vec{a} \) is always in the plane of \( \vec{a} \) and \( \vec{b} \) and is perpendicular to \( \vec{a} \).

Answer 1

The Correct Option is D