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Show that the points A (-2,3,5), B (1,2,...

Show that the 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 A =(2,3,5), B=(1,2,3) and (7,0,-1)
`therefore AB=sqrt((1+2)^(2)+(2-3)^(2)+(3+5)^(2))`
`=sqrt(9+1+4)=sqrt(14)` unit
`BC=sqrt((7-1)^(2)+(0-2)^(2)+(-1-3)^(2))`
`=sqrt(36+4+16)=sqrt(56)=2sqrt(14)`unit
`CA=sqrt((-2-7)^(2)+(3-0)^(2)+(5+1)^(2))`
`=sqrt(81+9+36)=sqrt(126)=3sqrt(14)` unit
Now, `AB+BC=sqrt(14)+2sqrt(14)=3sqrt(14)=CA`
`implies` Given points are collinear.
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