Consider the points $$A = (2, 1,-2)$$ and $$B = (1,-2, 3)$$, and find the parametric equations of the straight line that goes through $$A$$ anb $$B$$.
See development and solution
Development:
We will start computing a director vector of the straight line: $$$\overrightarrow{AB}=B-A=(1,-2,3)-(2,1,-2)=(-1,-3,5)$$$
Therefore, with the director vector and point $$A$$, we obtain the parametric equations: $$$\left\{\begin{array}{l} x=2-k \\ y=1-3k \\ z=-2+5k \end{array}\right.$$$
Solution:
$$\left\{\begin{array}{l} x=2-k \\ y=1-3k \\ z=-2+5k \end{array}\right.$$