空间直线方程的参数式(B009)

问题

若空间直线方程过点 $(x_{0}, y_{0}, z_{0})$, 且该直线的方向向量 $\vec{s}$ $=$ $(A, B, C)$, 则如何使用参数式方程表示该直线?

选项

[A].   $\left\{\begin{matrix} x = x_{0} + A,\\ y = y_{0} + B,\\ z = z_{0} + C.\end{matrix}\right.$

[B].   $\left\{\begin{matrix} x = x_{0} + At,\\ y = y_{0} + Bt,\\ z = z_{0} + Ct.\end{matrix}\right.$

[C].   $\left\{\begin{matrix} x = x_{0} + \frac{A}{t},\\ y = y_{0} + \frac{B}{t},\\ z = z_{0} + \frac{C}{t}.\end{matrix}\right.$

[D].   $\left\{\begin{matrix} x = Ax_{0},\\ y = By_{0},\\ z = Cz_{0}.\end{matrix}\right.$



显示答案

$\left\{\begin{matrix} \textcolor{red}{x} = \textcolor{orange}{x_{0}} + \textcolor{cyan}{A} \textcolor{yellow}{t},\\ \textcolor{red}{y} = \textcolor{orange}{y_{0}} + \textcolor{cyan}{B} \textcolor{yellow}{t},\\ \textcolor{red}{z} = \textcolor{orange}{z_{0}} + \textcolor{cyan}{C} \textcolor{yellow}{t}.\end{matrix}\right.$

其中,$t$ 为参数.