On the exterior of a tetrahedron, one vector is erected perpendicularly to each face, pointing outwards, and its length is equal to the area of the face. Show that the sum of these four vectors is 0.
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Can anyone please show me how to set this up? I was told that:
"The 4 vectors will be of equal magnitude but each of the two will be going in the opposite direction, hence they cancel each other out. 2 vectors cancel each other out and the other 2 also cancel each other out which gives us a sum of 0."

Question

On the exterior of a tetrahedron, one vector is erected perpendicularly to each face, pointing outwards, and its length is equal to the area of the face. Show that the sum of these four vectors is 0.
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Can anyone please show me how to set this up? I was told that: 
"The 4 vectors will be of equal magnitude but each of the two will be going in the opposite direction, hence they cancel each other out. 2 vectors cancel each other out and the other 2 also cancel each other out which gives us a sum of 0."

anonymous · Answer

Four vectors are erected perpendicularly to the four faces of a general tetrahedron. Each vector is pointing outwards and has length equal to the area of the face. Show that the sum of these four vectors is 0.
 
I received a hint: Let A, B, and C be vectors representing the three edges starting from a fixed vertex. Show that the sum of the four vectors is the zero vector. Do not introduce a coordinate system