Using the section formula, prove that the three pints `A(-2,3,5),B(1,2,3)a n d C(7,0,-1)` are collinear.

Explanation

Suppose the given points are collinear and C divides AB in the ratio `lambda`:1. Then, coordinates of C are


`(lambda−2)/(lambda+1), (2lambda+3)/(lambda+1), (3lambda+5)/(lambda+1)`


But, coordinates of C are (7,0,-1).


So,` (lambda−2)/(lambda+1)=7, (2lambda+3)/(lambda+1)=0 `and `(3lambda+5)/(lambda+1)=−1`


...