Vectors Questions (152)

Volume of parallelopiped determined by vectors $\vec{a},\vec{b},\vec{c}$ is 5. Then volume determined by $3(\vec{a}+\vec{b})$, $(\vec{b}+\vec{c})$ and $2(\vec{c}+\vec{a})$ is

Let $\vec{a}=(3-4\cos\theta)\hat{i}-(4\sin\theta)\hat{j}$, $\vec{b}=(4-5\sin\theta)\hat{i}-(5\cos\theta)\hat{j}$, for $\theta\in\left(0,\frac{\pi}{2}\right)$. Then the least value of $|\vec{a}|+|\vec{b}|$ is