1.

Prove that the points `A(3,-2,4) , B(3,-2,4), B(1,1,1) and C(-1,4,-2)` are collinear.

Answer» We have,
`AB=sqrt((1-3)^(2)+(1+2)^(2)+(1-4)^(2))=sqrt(4+9+9)=sqrt(22)`
`BC=sqrt((1-1)^(2)+(4-1)^(2)+(-2-1)^(2))=sqrt(4+9+9)=sqrt(22)`
`and AC=sqrt((1-3)^(2)+(4-2)^(2)+(-2-4)^(2))=sqrt(16+36+36)`
`=sqrt(88)=2sqrt(22)`
` :. AB+BC+AC`
This show that the given points are collinear.


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