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Using section formula, show that the po...

Using section formula, show that the points `A (2, -3, 4)`, `B (-1, 2, 1)`and `C(0,1/3,2)`are collinear.

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The correct Answer is:
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Let point C divides the line segment joining the points A and B in the ratio k : 1.
`therefore 0=(k(-1)+1(2))/(k+1) implies -k+2=0 implies k=2`
`(1)/(3)=(k(2)+1(-3))/(k+1) implies 6k-9=k+1 implies k=2`
`2=(k(1)+1(4))/(k+1) implies 2k+2=k+4 implies k=2`
We get k=2 from each.
Therefore, given points are collinear.
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