Question

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

Answer 1

Let $A(5,4,2),B(6,2,-1)$ and $C(8,-2,-7)$

$\overline{AB}=\overrightarrow{i}-2\overrightarrow{j}-3\overrightarrow{k}$

$\overline{BC}=2\overrightarrow{i}-4\overrightarrow{j}-6\overrightarrow{k}$

$\overline{BC}=2\overline{AB}\Rightarrow$ Points $A,B$ and $C$ are collinear.