Scalar triple product
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Co-planar points
Equations are omitted for technical reasons - download the original pdf
If four points are not planar, they define a parallelepiped with non-zero volume. [Diagram goes here - download the original to see it.] So, if the volume of the parallelepiped defined by four points is zero, then the parellelepiped has "collapsed" and the points must be coplanar. If the position vectors of the points are a, b, c and d respectively, then the requirement that the volume of the parallelepiped be zero gives [Diagram goes here - download the original to see it.] [Equation goes here - download the original to see it.]
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Contents of
Scalar triple product
1 Scalar Triple Product
2 The triple scalar product as a "signed" volume
3 Shortest distance between two skew lines
4 Intersecting and parallel lines
5 Co-planar points
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