Let a and b be two unit vectors such that the angle between them is (π)/3. If λ a +2 b and 3 a -λ b are perpendicular to each other, then the number…

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