(4) Given that $\vec{a}$ and $\vec{b}$ are non-zero and non-collinear vectors, let condition $M: \vec{b} \perp (\vec{a}-\vec{b})$;
condition $N$: for all $x \in \mathbf{R}$, the inequality $|\vec{a}-x \vec{b}| \geqslant |\vec{a}-\vec{b}|$ always holds. Then $M$ is ( ) of $N$.
(A) a necessary but not sufficient condition
(B) a sufficient but not necessary condition
(C) a sufficient and necessary condition
(D) neither a sufficient nor a necessary condition