空间直线方程的两点式(B009)

问题

若空间直线方程过点 $(x_{1}, y_{1}, z_{1})$ 和 $(x_{2}, y_{2}, z_{2})$, 则如何使用 [两点式方程] 表示该直线?

选项

[A].   $\frac{x – x_{2}}{x_{2} – x_{1}}$ $=$ $\frac{y – y_{2}}{y_{2} – y_{1}}$ $=$ $\frac{z – z_{2}}{z_{2} – z_{1}}$

[B].   $\frac{x – x_{1}}{x – x_{2}}$ $=$ $\frac{y – y_{1}}{y – y_{2}}$ $=$ $\frac{z – z_{1}}{z – z_{2}}$

[C].   $\frac{x + x_{1}}{x_{2} + x_{1}}$ $=$ $\frac{y + y_{1}}{y_{2} + y_{1}}$ $=$ $\frac{z + z_{1}}{z_{2} + z_{1}}$

[D].   $\frac{x – x_{1}}{x_{2} – x_{1}}$ $=$ $\frac{y – y_{1}}{y_{2} – y_{1}}$ $=$ $\frac{z – z_{1}}{z_{2} – z_{1}}$



显示答案

$\frac{\textcolor{red}{x} – \textcolor{cyan}{x_{1}}}{\textcolor{orange}{x_{2}} – \textcolor{cyan}{x_{1}}}$ $=$ $\frac{\textcolor{red}{y} – \textcolor{cyan}{y_{1}}}{\textcolor{orange}{y_{2}} – \textcolor{cyan}{y_{1}}}$ $=$ $\frac{\textcolor{red}{z} – \textcolor{cyan}{z_{1}}}{\textcolor{orange}{z_{2}} – \textcolor{cyan}{z_{1}}}$