JEE Advanced 2020 — Paper 1 — Question 43

In a triangle $P Q R$, let $\vec{a}=\overrightarrow{Q R}, \vec{b}=\overrightarrow{R P}$ and $\vec{c}=\overrightarrow{P Q}$. If

$|\overrightarrow{\mathrm{a}}|=3,|\overrightarrow{\mathrm{~b}}|=4 \text { and } \frac{\overrightarrow{\mathrm{a}} \cdot(\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{b}})}{\overrightarrow{\mathrm{c}} \cdot(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}})}=\frac{|\overrightarrow{\mathrm{a}}|}{|\overrightarrow{\mathrm{a}}|+|\overrightarrow{\mathrm{b}}|},$ then the value of $|\vec{a} \times \vec{b}|^{2}$ is $\_\_\_\_$