How to know four vectors are coplanar?

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Answer:-
Let four points are A,B,C,D which are lies in one plane.the position vector of their with respect to origin are OA,OB,OC & OD respectively.
Now,AB=OB-OA
        AC=OC-OA
         AD=OD-OA
We know 1/6{AB•(AC×AD)} gives the volume of tetrahedron. if four vectors lies in one plane(coplanar) then their volume is zero[i.e AB•(AC×AD)=0].
So to prove the given four vectors are coplanar we have to show the determinant of AB•(AC×AD) is zero.


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