问题
若已知空间曲线 $\Gamma$ 的一般式方程为 $\left\{\begin{array}{l} F(x, y, z)=0, \\ G(x, y, z)=0 \end{array}\right.$, 则在曲线 $\Gamma$ 上的点 $(x_{0}, y_{0}, z_{0})$ 处，曲面 $F(x, y, z)$ $=$ $0$ 和 $G(x, y, z)$ $=$ $0$ 的两个法向量 $n_{1}$ 和 $n_{2}$ 分别是多少？选项
[A]. $\boldsymbol{n}_{1}$ $=$ $($ $F_{x x}^{\prime \prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $F_{y y}^{\prime \prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $F_{z z}^{\prime \prime}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$$\boldsymbol{n}_{2}$ $=$ $($ $G_{x x}^{\prime \prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $G_{y y}^{\prime \prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $G_{z z}^{\prime \prime}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$
[B]. $\boldsymbol{n}_{1}$ $=$ $($ $- F_{x}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $- F_{y}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $- F_{z}^{\prime}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$
$\boldsymbol{n}_{2}$ $=$ $($ $- G_{x}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $- G_{y}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $- G_{z}^{\prime}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$
[C]. $\boldsymbol{n}_{1}$ $=$ $($ $F_{x}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $F_{y}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $F_{z}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$
$\boldsymbol{n}_{2}$ $=$ $($ $G_{x}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $G_{y}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $G_{z}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$
[D]. $\boldsymbol{n}_{1}$ $=$ $($ $F_{x}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $F_{y}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $F_{z}^{\prime}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$
$\boldsymbol{n}_{2}$ $=$ $($ $G_{x}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $G_{y}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $G_{z}^{\prime}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$
$\boldsymbol{n}_{1}$ $=$ $($ $F_{x}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $F_{y}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $F_{z}^{\prime}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$
$\boldsymbol{n}_{2}$ $=$ $($ $G_{x}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $G_{y}^{\prime}$ $($ $x_{0}, y_{0}, z_{0}$ $)$, $G_{z}^{\prime}$ $(x_{0}, y_{0}, z_{0}$ $)$ $)$