Lesson Plan: Scalar Triple Product Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to calculate the scalar triple product and apply this in geometrical applications.


Students will be able to

  • understand and use the fact that the scalar triple product is equivalent to a 3×3 determinant,
  • calculate the scalar triple product of three vectors,
  • understand that the absolute value of the scalar triple product between three vectors represents the volume of the parallelepiped spanned by the three vectors,
  • apply the properties of the scalar triple product to solve geometrical problems, including proving that vectors are coplanar.


Students should already be familiar with

  • the dot product in space,
  • the cross product in space,
  • 3×3 determinants.


Students will not cover

  • vectors’ triple product,
  • vectors represented in a column matrix.

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