## 4 vectors perpendicular to four faces of tetrahedron. Show that the sum = zero vector

1. The problem statement, all variables and given/known data
Four vectors are erected perpendicular to the four faces of a general tetrahedron. Each vector is pointing outwards and has a length equal to the area of the face. Show that the sum of these four vectors is zero.

2. Relevant equations

3. The attempt at a solution
Let A, B and C be vectors representing the three edges starting from a fixed vertex. Then, express each of the four vectors in terms of A, B and C.
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 I figured out how to do the problem. But there's another part to the problem: Formulate and prove the analogous statement for a plane triangle. What is meant by a "planar triangle"?
 Recognitions: Homework Help i think it probably just means any normal triangle (normal in the sense that it is contained within in a plane in R^3, so planar) can you show it for such? where i'm guessing the analogy is area to length

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## 4 vectors perpendicular to four faces of tetrahedron. Show that the sum = zero vector

Put your triangle in the xy plane; label the vertices A,B,C clockwise. Make vectors of the sides going from A to B, B to C, C to A (i.e, $\vec a = B - A$ etc.). Those side vectors add to the zero vector. Now rotate the triangle 90 degrees counterclockwise and they become perpendicular to the original sides pointing outward and the right length. Presto!
 I am trying to solve this same problem. Would the person who asked the question and said he/she figured it out please tell me how its done? Unfortunately, it is just not clicking with me. Thank you.
 Could you explain how you solved this?

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