Question

Using the section formula, prove that the three points
A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1) are collinear.

Answer 1

Suppose C divides AB in the ratio $\lambda :1$.

Then, $\frac{\lambda -2}{\lambda +1}=7,\frac{2\lambda +3}{\lambda +1}=0$ and $\frac{3\lambda +5}{\lambda +1}=-1$

From each of these equations, we get $\lambda =\frac{-3}{2}$.

This shows that C divides AB externally in the ratio 3:2.

So, C lies on the line joining A and B.

Hence, the given points A, B, C are collinear.