Q. 3 A4.3( 3 Votes )

Show that the following points are coplanar.

(0, – 1, 0), (2, 1, – 1), (1, 1, 1) and (3, 3, 0)

Answer :

Given that these four points are coplanar so these four points lie on the same plane


So first let us take three points and find the equation of plane passing through these four points and then let us substitute the fourth point in it. If it is 0 then the point lies on the plane formed by these three points then they are coplanar.


the equation of the plane passing through these three points is given by the following equation.



Now let us take (0, – 1, 0), (2, 1, – 1), (1, 1, 1) and find plane equation.




Now apply the determinant



x(2 + 2) – (y + 1)(2 + 1) + z(4 – 2) = 0


4x – 3y – 3 + 2z = 0


4x – 3y + 2z – 3 = 0


Now let us substitute (3, 3, 0) in plane equation


4x – 3y + 2z – 3 = 0


4(3) – 3(3) + 2(0) – 3 = 0


12 – 9 + 0 – 3 = 0


12 – 12 = 0


0 = 0


So this point lies on the plane


Hence they are coplanar.


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