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Let \(\hat{u}\) and \(\hat{v}\) be unit vectors inclined at an acute angle such that \(|\hat{u}\times \hat{v}|=\frac{\sq…

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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 \(\vec{A}=\lambda \hat{u}+\hat{v}+\left(\hat{u}\times \hat{v}\right)\), then \(\lambda\) is equal to:

[JEE Main 2026, 4 Apr (Shift 2)]

a

\(\frac{4}{3}\left(\vec{A}\cdot \hat{u}\right)-\frac{2}{3}\left(\vec{A}\cdot \hat{v}\right)\)

b

\(\frac{2}{3}\left(\vec{A}\cdot \hat{u}\right)-\frac{1}{3}\left(\vec{A}\cdot \hat{v}\right)\)

c

\(\frac{4}{3}\left(\vec{A}\cdot \hat{u}\right)+\frac{2}{3}\left(\vec{A}\cdot \hat{v}\right)\)

d

\(\left(\vec{A}\cdot \hat{u}\right)-\frac{1}{2}\left(\vec{A}\cdot \hat{v}\right)\)

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