I read all posts online regarding how to show four points are coplanar. However, none of them discuss the idea behind the method. Can someone explain how the triple scalar product works?

You are watching: How to determine if points are coplanar

You know that three points \$A,B,C\$ (two vectors \$vecAB\$, \$vecAC\$) form a plane. If you want to show the fourth one \$D\$ is on the same plane, you have to show that it forms, with any of the other point already belonging to the plane, a vector belonging to the plane (for instance \$vecAD\$).

Since the cross product of two vectors is normal to the plane formed by the two vectors (\$vecAB imes vecAC\$ is normal to the plane \$ABC\$), you just have to prove your last vector \$vecAD\$ is normal to this cross product, hence the triple product that should be equal to \$0\$:

Thanks for contributing an answer to les-grizzlys-catalans.orgematics Stack Exchange!

But avoid

Asking for help, clarification, or responding to other answers.Making statements based on opinion; back them up with references or personal experience.

Use les-grizzlys-catalans.orgJax to format equations. les-grizzlys-catalans.orgJax reference.

## Not the answer you're looking for? Browse other questions tagged linear-algebra or ask your own question.

site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. rev2021.11.1.40614

See more: How To Set Clock On Pioneer Radio Mosfet 50Wx4 ? How Do I Set The Clock On My Single Cd Player

les-grizzlys-catalans.orgematics Stack Exchange works best with JavaScript enabled