14. Given $|\vec{a}|=3,|\vec{b}|=2, \vec{a}$ and $\vec{b}$ have an angle of $\frac{\pi}{3}$ between them.
(1) Find the value of $|3 \vec{a}-2 \vec{b}|$;
(2) If $\vec{c}=3 \vec{a}+5 \vec{b}, \vec{d}=m \vec{a}-3 \vec{b}$, for what value of $m$ is $\vec{c} \perp \vec{d}$.
14. (1) $\vec{a} \cdot \vec{b}=3$, $|3 \vec{a}-2 \vec{b}|^{2}=9 \vec{a}^{2}-12 \vec{a} \cdot \vec{b}+4 \vec{b}^{2}=61$;
(2) $\vec{c} \cdot \vec{d}=(3 \vec{a}+5 \vec{b}) \cdot(m \vec{a}-3 \vec{b})=3m \vec{a}^{2}+(5m-9) \vec{a} \cdot \vec{b}-15 \vec{b}^{2}=42m-87=0$, get $m=\frac{29}{14}$.