Consider the points $$A = (2, 1,-2)$$ and $$B = (1,-2, 3)$$, and find the continuous 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 continuous equation: $$$\dfrac{x-2}{-1}=\dfrac{y-1}{-3}=\dfrac{z+2}{5}$$$
Solution:
Continuous equation: $$\dfrac{x-2}{-1}=\dfrac{y-1}{-3}=\dfrac{z+2}{5}$$