Question

Find the equation of line passing through $(5,0,5)$ & $(2,1,3)$. Also show that $(5,0,5),(2,1,3)$ & $(-4,3,-1)$ are collinear.

Answer 1

Equation of line passing through $(5,0,5)$ and $(2,1,3)$is:

$\frac{x-5}{3}=\frac{y-0}{-1}=\frac{z-5}{2}(x,y,z)\equiv (-4,3,-1)\frac{-4-5}{3}=\frac{3}{-1}=\frac{-1-5}{2}=-3$

$\therefore$ point $(-4,3,-1)$ satisfies equation of line hence the three points $(5,0,5),(2,1,3)$ & $(-4,3,-1)$ are collinear as they fall on one same line.