The points `P(3,2,4), Q(4,5,2), R(5,8,0) and S(2,-1,6)` are

Options

A. vertices of a rhombus which is not a square
B. non-coplanar
C. collinear
D. copanar but not collinear

Answer

C

Explanation

`P(3,2,4), Q(4,5,2), R(5,8,0), S(2,-1,6)`
`PQ=sqrt((4-3)^2+(5-2)^2+(2-4)^2)`
`=sqrt(1+9+4)=sqrt14`
`QR=sqrt((5-4)^2+(8-5)^2+(0-2)^2)`
`=sqrt(1+9+4)=sqrt14`
`RS=sqrt((2-5)^2+(-1-8)^2+(6-0)^2)`
`=sqrt(9+81+4)=sqrt14`
`PS=sqrt((2-3)^2+(-1-2)^2+(6-4)^2)`
`=sqrt(1+9+4)=sqrt14`

Since, `PQ + QR - PS=RS`, points are collinear.