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Four Points are on a Plane if the Scalar Triple Product is Zero

If 4 points are on a plane then the volume of the parallelepiped (determined by the scalar triple product) spanned by their position vectors is zero.

Watch on YouTube - Video notes - Video sections playlist - Vectors and the Geometry of Space playlist

In this video I illustrate a method for determining of 4 points lie on the same plane by checking if their scalar triple product (or volume of a parallelepiped) is zero. If it is zero then it means the volume of the parallelepiped spanned by the position vectors between the 4 points is zero, aka a flat plane.

Timestamps:

  • Question 16 (b): 4 4oints on a plane: 0:00

  • Solution: Volume of parallelepiped (scalar triple product) is zero: 0:13

  • Illustration of method: 1:2

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