Let u and v be unit vectors inclined at an acute angle such that | u × v |=(√ 3)/2. If A =λ u + v +( u × v ), then λ is equal to:

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