设 $\mathbf{a}, \mathbf{b}, \mathbf{c}$ 不共面，且向量 $\mathbf{r}$ 满足
$$
\mathbf{a} \cdot \mathbf{r}=\alpha, \mathbf{b} \cdot \mathbf{r}=\beta, \mathbf{c} \cdot \mathbf{r}=\gamma
$$
那么有 $\mathbf{r}=\frac{1}{(\mathbf{a}, \mathbf{b}, \mathbf{c})}[\boldsymbol{\alpha}(\mathbf{b} \times \mathbf{c})+\boldsymbol{\beta}(\mathbf{c} \times \mathbf{a})+\gamma(\mathbf{a} \times \mathbf{b})]$ ．
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$
$\text{E.}$
$\text{F.}$