4.   Using section formula, show that the points A (2, –3, 4), B (–1, 2, 1) and C \left ( 0 , 1/3 , 2 \right ) are collinear.

Answers (1)
P Pankaj Sanodiya

Given, 

three points, A (2, –3, 4), B (–1, 2, 1) and C (0, 1/3, 2)

Let a point P divides Line segment AB in the ratio \lambda:1

SO, according to the section formula, the point P will be 

\left (\frac{-\lambda +2}{\lambda+1},\frac{2\lambda-3}{\lambda+1},\frac{\lambda+4}{\lambda+1} \right )

Now, let's compare this point P with point C.

\frac{-\lambda +2}{\lambda+1},=0

\lambda=2

From here, we see that for \lambda=2, point C divides the line segment AB in ratio 2:1. Since point C divides the line segment AB, it lies in the line joining A and B and Hence they are colinear.

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