1. In the parallelepiped $A B C D-A_{1} B_{1} C_{1} D_{1}$, $M$ is the intersection of $A_{1} C_{1}$ and $B_{1} D_{1}$. If $\boldsymbol{A B}=\boldsymbol{a}, \boldsymbol{A D}=\boldsymbol{b}, \boldsymbol{A} \boldsymbol{A}_{1}=\boldsymbol{c}$, then among the following vectors, the vector equal to $\boldsymbol{B} \boldsymbol{M}$ is ( ).
(A) $-\frac{1}{2} a+\frac{1}{2} b+c$
(B) $\frac{1}{2} a+\frac{1}{2} b+c$
(C) $-\frac{1}{2} a-\frac{1}{2} b+c$
(D) $\frac{1}{2} a-\frac{1}{2} b+c$
$$
-\mathbf{1 . A} .
$$

It is easy to calculate $B M=-\frac{1}{2} a+\frac{1}{2} b+c$.