Mathematics - Vector Question with Solution | TestHub

Consider three vectors $\vec{a},\vec{b},\vec{c}$. Let $|\vec{a}|=2,|\vec{b}|=3$ and $\vec{a}=\vec{b}\times \vec{c}$. If $\alpha \in \left[0,\frac{\pi }{3}\right]$ is the angle between the vectors $\vec{b}$ and $\vec{c}$, then the minimum value of $27|\vec{c}-\vec{a}{|}^2$ is equal to: