Question

Show that the points $(5,4,2),(6,2,-1)$ and $(8,-2,-7)$ are collinear.

Answer 1

Given $(5,4,2),(6,2,-1),(8,-2,-7)$

$(x_1,y_1,z_1)=(5,4,2)$

$(x_2,y_2.z_2)=(6,2,-1)$

$(x_3,y_3,z_3)=(8,-2,-7)$

$\frac{x_1-x_2}{x_2-x_3}=\frac{y_1-y_2}{y_2-y_3}=\frac{z_1-z_2}{z_2-z_3}$

$\frac{5-6}{6-8}=\frac{4-2}{2+2}=\frac{2+1}{-1+7}$

$\frac{-1}{-2}=\frac{2}{4}=\frac{3}{6}$

$\frac{1}{2}=\frac{1}{2}=\frac{1}{2}$

$\therefore$ they are collinear