Lesson Plan: Cross Product in 3D Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the cross product of two vectors in space and how to use it to find the area of geometric shapes.


Students will be able to

  • define the cross product of two vectors as the product of the magnitudes multiplied by the sine of the angle between the vectors,
  • calculate the cross product of two vectors in space using their components (i.e., a 3×3 determinant),
  • understand the properties of the cross product in 3D,
  • use the geometric meaning of cross product to solve problems, in particular, finding lengths or areas.


Students should already be familiar with

  • adding and subtracting vectors in 3D,
  • dot product in 3D,
  • 3×3 determinants.


Students will not cover

  • parallelism condition using vector product,
  • scalar triple product,
  • vector triple product.

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