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 $n_{2}$ 分别为：$\boldsymbol{n}_{1}$ $=$ $\left(F_{x}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), F_{y}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), F_{z}^{\prime}\left(x_{0}, y_{0}, z_{0}\right)\right)$
$\boldsymbol{n}_{1}$ $=$ $\left(G_{x}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), G_{y}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), G_{z}^{\prime}\left(x_{0}, y_{0}, z_{0}\right)\right)$,
则曲线 $\Gamma$ 在点 $(x_{0}, y_{0}, z_{0})$ 处的切向量 $\boldsymbol{\tau}$ $=$ $?$
选项
[A]. $\boldsymbol{\tau}$ $=$ $\boldsymbol{n}_{1} – \boldsymbol{n}_{2}$[B]. $\boldsymbol{\tau}$ $=$ $\boldsymbol{n}_{1} \div \boldsymbol{n}_{2}$
[C]. $\boldsymbol{\tau}$ $=$ $\boldsymbol{n}_{1} \times \boldsymbol{n}_{2}$
[D]. $\boldsymbol{\tau}$ $=$ $\boldsymbol{n}_{1} + \boldsymbol{n}_{2}$
$\boldsymbol{\tau}$ $=$ $\boldsymbol{n}_{1} \times \boldsymbol{n}_{2}$