Let \( \hat{u} \) and \( \hat{v} \) be unit vectors inclined at an acute angle such that \( \left|\hat{u}\times\hat{v}\right|=\frac{\sqrt{3}}{2} \). If \( \vec{A}=\lambda \hat{u}+\hat{v}+(\hat{u}\times\hat{v}) \), then \( \lambda \) is equal to:
\( \frac{4}{3}(\vec{A}\cdot\hat{u})-\frac{2}{3}(\vec{A}\cdot\hat{v}) \)
\( \frac{2}{3}(\vec{A}\cdot\hat{u})-\frac{1}{3}(\vec{A}\cdot\hat{v}) \)
\( \frac{4}{3}(\vec{A}\cdot\hat{u})+\frac{2}{3}(\vec{A}\cdot\hat{v}) \)
\( (\vec{A}\cdot\hat{u})-\frac{1}{2}(\vec{A}\cdot\hat{v}) \)
