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Using section formula, prove that the th...

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

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The correct Answer is:
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Let B divides AC in the ratio `lamda : 1`.

`therefore " Co-ordinates of B"=((7lamda-2)/(lamda+1),(3)/(lamda+1),(-lamda+5)/(lamda+1))`
Now, `(7lamda-2)/(lamda+1)=1, (3)/(lamda+1)=2, (-lamda+5)/(lamda+1)=3`
`implies lamda=(1)/(2)` which can be obtained from each equation
Therefore, B divides AC in the ratio 1 : 2.
`implies A, B` and C are collinear.
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