(3) Given that $\vec{a}$ and $\vec{b}$ are both unit vectors, and their included angle is $\theta$, then the proposition $p:|\vec{a}-\vec{b}|>$ 1 , is the proposition $q: \theta \in\left[\frac{\pi}{2}, \frac{5 \pi}{6}\right)$ ( ).
(A) sufficient but not necessary condition
(B) necessary but not sufficient condition
(C) sufficient and necessary condition
(D) neither sufficient nor necessary condition
(3) B Hint: From the geometric meaning of vectors, we know that $|\vec{a}-\vec{b}|>1 \Rightarrow \theta \in\left(\frac{\pi}{3}, \pi\right)$; if
$$
\theta \in\left[\frac{\pi}{2}, \frac{5 \pi}{6}\right) \Rightarrow|\vec{a}-\vec{b}|>1 .
$$