JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 29

Let $\vec a$ and $\vec b$ be two vectors such that $|\vec a+\vec b|^2=|\vec a|^2+2|\vec b|^2$, $\vec a\cdot\vec b=3$ and $|\vec a\times\vec b|^2=75$. Then $|\vec a|^2$ is equal to _______.