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Using the section formula, prove that th...

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.

Text Solution

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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`
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