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Let \(\overset{^}{u}\) and \(\overset{^}{v}\) be unit vectors inclined at an acute angle such that \(|\overset{^}{u}\tim…

Q1

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

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

a

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

b

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

c

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

d

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

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