Question

Using section formula. prove that the three points (-4,6,10),(2,4,6) and (14,0,-2) are collinear.

Answer 1

Let $\Rightarrow 2=\frac{14k-4}{k+1}$

$\Rightarrow 14k-4=2k+2$

$\Rightarrow 12k=6$

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

and $4=\frac{0+6}{k+1}$

$\Rightarrow 4k+4=6$

$\Rightarrow 4k=2$

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

and $6=\frac{-2k+10}{k+1}$

$\Rightarrow 6k+6=-2k+10$

$\Rightarrow 8k=4$

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

$\Rightarrow B(2,4,6)$ divides AC in $1:2$

$\Rightarrow$ A, B, C are collinear.