Answer to Question #125579 in Analytic Geometry for Fiyin

Question

Find the parametric equation of the line that passes through the points (0,1,1) and (1,0,-1).

Answer 1

Soiution:

$\begin{cases} x=x_1+(x_2-x_1)\times\lambda \\ x=y_1+(y_2-y_1)\times\lambda \\ z=z_1+(z_2-z_1)\times\lambda \\ \end{cases} \Rightarrow\\ \Rightarrow \begin{cases} x=0+(1-0)\times\lambda \\ у=1+(0-1)\times\lambda \\ z=1+(-1-1)\times\lambda \\ \end{cases} \Rightarrow \\ \Rightarrow \begin{cases} x=\lambda \\ у=1-\lambda \\ z=1-2\times\lambda \\ \end{cases} \\Answer: \\\;\;\;\;\; \begin{cases} x=\lambda \\ у=1-\lambda \\ z=1-2\times\lambda \\ \end{cases}$