Vectors · Scalar and vector products

Let

\hat u

and

\hat v

be unit vectors inclined at an acute angle such that

\lvert\hat u \times \hat v\rvert = \dfrac{\sqrt3}{2}

. If

\vec A = \lambda\hat u + \hat v + (\hat u \times \hat v)

. Then

\lambda

is equal to:

(1) $\dfrac43\left(\vec A\cdot\hat u\right) - \dfrac23\left(\vec A\cdot\hat v\right)$
(2) $\dfrac23\left(\vec A\cdot\hat u\right) - \dfrac13\left(\vec A\cdot\hat v\right)$
(3) $\dfrac43\left(\vec A\cdot\hat u\right) + \dfrac23\left(\vec A\cdot\hat v\right)$
(4) $\left(\vec A\cdot\hat u\right) - \dfrac12\left(\vec A\cdot\hat v\right)$

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