Question

Using section formula prove that the point $(\mathrm{0.7.}-7),(1,4,-5)$ and $(-1,10,-9)$ are collinear.

Answer 1

$A(0,7,-7),B(1,4,-5),C(-1,10,-9)$

$\overrightarrow{AB}=\hat{i}-3\hat{j}+2\hat{b}$

$\overrightarrow{AC}=-\hat{i}-3\hat{j}-2\hat{b}$

$=-(\hat{i}-3\hat{j}+2\hat{b})$

$\overrightarrow{AB}=(-1)\overrightarrow{AC}$

$\therefore A,B,C$ are collinear