coplanarity

Question

Four points are coplanar if the volume of tetrahedron formed by them is

RankGuru · Accepted Answer

1. **Theory**: If four points $A, B, C, D$ lie in the same plane, they have no 'height' relative to each other in 3D space.
2. **Volume Property**: The volume of a tetrahedron formed by three vectors $\vec{AB}, \vec{AC}, \vec{AD}$ is $V = \frac{1}{6} |\vec{AB} \cdot (\vec{AC} 	imes \vec{AD})|$.
3. **Result**: If the points are coplanar, the vectors are linearly dependent and the scalar triple product is zero, thus $V = 0$.

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coplanarity

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