Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors such that the angle between them is \(\frac{\pi}{3}\). If \(\lambda …

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors such that the angle between them is \(\frac{\pi}{3}\). If \(\lambda \vec{a}+2 \vec{b}\) and \(3 \vec{a}-\lambda \vec{b}\) are perpendicular to each other, then the number of values of \(\lambda\) in \([-1,3]\) is :

[JEE Main 2025, 22 Jan (Shift 2)]