For a triangle ABC, let p = B C, q = C A and r = B A. If | p |=2 √ 3,| q |=2 and cos θ=1/(√ 3), where θ is the angle between p and q, then | p ×( q…

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