Vector Algebra: JEE Main 2026 Mathematics question

For a triangle ABC, let $\vec{p}=\overrightarrow{BC}$, $\vec{q}=\overrightarrow{CA}$ and $\vec{r}=\overrightarrow{BA}$. If $|\vec{p}|=2\sqrt{3}$, $|\vec{q}|=2$ and $\cos\theta=\frac{1}{\sqrt{3}}$, where $\theta$ is the angle between $\vec{p}$ and $\vec{q}$, then $\left|\vec{p}\times(\vec{q}-3\vec{r})\right|^2+3|\vec{r}|^2$ is equal to :