jee-main 2026 Q15

jee-main · India · session1_21jan_shift2 Vectors 3D & Lines Vector Algebra and Triple Product Computation
If three vectors are given as shown. If angle between vector $\vec{p}$ and $\vec{q}$ is $\theta$ where $\cos\theta = \frac{1}{\sqrt{3}}$ and $|\vec{p}| = 2\sqrt{3}$, $|\vec{q}| = 2$. Then the value of $|\vec{p} \times (\vec{q} - 3\vec{r})|^2 - 3|\vec{r}|^2$ is
If three vectors are given as shown. If angle between vector $\vec{p}$ and $\vec{q}$ is $\theta$ where $\cos\theta = \frac{1}{\sqrt{3}}$ and $|\vec{p}| = 2\sqrt{3}$, $|\vec{q}| = 2$. Then the value of $|\vec{p} \times (\vec{q} - 3\vec{r})|^2 - 3|\vec{r}|^2$ is