Proving Vector OA + OB + OC Perpendicularity in Regular Tetrahedrons

[jaejoon89]

"The vertices of a regular tetrahedron are OABC. Prove that vector OA + OB + OC is perpendicular to plane ABC."

---

No idea how to do this. Please help.

 

[Mark44]

Each face of a regular tetrahedron is an equilateral triangle. There is one face at the bottom and three other faces making four faces in all. Each interior angle of an equilateral triangle is 60 degrees.

Can you use this information to find the coordinates of the vertices of your tetrahedron? Once you have them, then you can add your three vectors together and see that their sum is perpendicular to the base.