Question

Let \(\hat{u}\) and \(\hat{v}\) be unit vectors inclined at an acute angle such that \(|\hat{u} \times \hat{v}| = \frac{\sqrt{3}}{2}\). If \(\vec{A} = \lambda \hat{u} + \hat{v} + (\hat{u} \times \hat{v})\), then \(\lambda\) is equal to:

• A. \(\frac{4}{3}(\vec{A} \cdot \hat{u}) - \frac{2}{3}(\vec{A} \cdot \hat{v})\)
• B. \(\frac{2}{3}(\vec{A} \cdot \hat{u}) - \frac{1}{3}(\vec{A} \cdot \hat{v})\)
• C. \(\frac{4}{3}(\vec{A} \cdot \hat{u}) + \frac{2}{3}(\vec{A} \cdot \hat{v})\)
• D. \((\vec{A} \cdot \hat{u}) - \frac{1}{2}(\vec{A} \cdot \hat{v})\)

Answer 1

The Correct Option is A