问题
若已知空间曲线 $\Gamma$ 的参数方程为 $\left\{\begin{array}{l}x=x(t), \\ y=y(t) \\ z=z(t)\end{array}\right.$, 则曲线 $\Gamma$ 在点 $(x_{0}, y_{0}, z_{0})$（对应参数 $t$ $=$ $t_{0}$）处的切线方程为多少？选项
[A]. $\frac{x-x_{0}}{x \left(t_{0} \right)}$ $=$ $\frac{y-y_{0}}{y \left(t_{0} \right)}$ $=$ $\frac{z-z_{0}}{z \left(t_{0} \right)}$[B]. $\frac{x+x_{0}}{x^{\prime}\left(t_{0} \right)}$ $=$ $\frac{y+y_{0}}{y^{\prime}\left(t_{0} \right)}$ $=$ $\frac{z+z_{0}}{z^{\prime}\left(t_{0} \right)}$
[C]. $\frac{x-x_{0}}{x^{\prime}\left(t_{0} \right)}$ $=$ $\frac{y-y_{0}}{y^{\prime}\left(t_{0} \right)}$ $=$ $\frac{z-z_{0}}{z^{\prime}\left(t_{0} \right)}$
[D]. $\frac{x-x_{0}}{x^{\prime \prime}\left(t_{0} \right)}$ $=$ $\frac{y-y_{0}}{y^{\prime \prime}\left(t_{0} \right)}$ $=$ $\frac{z-z_{0}}{z^{\prime \prime}\left(t_{0} \right)}$
$\frac{x-x_{0}}{x^{\prime}\left(t_{0} \right)}$ $=$ $\frac{y-y_{0}}{y^{\prime}\left(t_{0} \right)}$ $=$ $\frac{z-z_{0}}{z^{\prime}\left(t_{0} \right)}$