Unit 10: Cross products
About this unit
In 2D, u × v is the signed area of the parallelogram u and v span, the determinant of [u v]. In 3D, u × v is a vector perpendicular to both whose length is that area and whose direction follows the right-hand rule; v × u = −(u × v).
By the end, you can: Read the 2D cross product as a signed area, and compute and picture the 3D cross product as a vector perpendicular to both inputs with length equal to their parallelogram's area.
Modules
5 modulesLearn
- Area with a signArticle · In 2D, u × v is the signed area of the parallelogram u and v span, equal to det[u v] = u₁v₂ − u₂v₁; it is positive when v is anticlockwise of u, negative when clockwise, and zero when they are parallel.Not started
- Turn the area negativeExperiment · Drag v until the signed area is −5 and see that only v's side of u and its height above u's line matter.Not started
- A vector out of two vectorsArticle · In 3D, u × v is a vector perpendicular to both, as long as their parallelogram's area, pointing by the right-hand rule; compute it by the component formula or the î, ĵ, k̂ determinant pattern.Not started
- Cross products in briefReview · The 2D signed area, the 3D vector, its length, direction and formula, and the sign rules.Not started