You are watching: How to determine if points are coplanar
You know that three points $A,B,C$ (two vectors $vecAB$, $vecAC$) form a plane. If you want to show the fourth one $D$ is on the same plane, you have to show that it forms, with any of the other point already belonging to the plane, a vector belonging to the plane (for instance $vecAD$).
Since the cross product of two vectors is normal to the plane formed by the two vectors ($vecAB imes vecAC$ is normal to the plane $ABC$), you just have to prove your last vector $vecAD$ is normal to this cross product, hence the triple product that should be equal to $0$:
$vecAD cdot(vecAB imes vecAC)=0$
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