Find a basis for 4 unit non co-planar vectors that exist in 3-D which sum to 0
A+B+C+D=0
*note (this must means not all 4 can be in the same plane, u can have upto 3 in the same plane just not all 4)

Here is an analog
3 unit vectors that sum to 0 in 2-D, are planar but non-colinear

A+B+C=0

For this to be true this means they must exist in the form of
$$e^{\frac {i2\pi k}{3}}=1, for ~k=0,1,2$$, there can be an additional phase angle to define all the possible basis
in 2-D

Question

Find a basis for 4 unit non co-planar vectors that exist in 3-D which sum to 0
A+B+C+D=0
*note (this must means not all 4 can be in the same plane, u can have upto 3 in the same plane just not all 4)

Here is an analog
3 unit vectors that sum to 0 in 2-D, are planar but non-colinear

A+B+C=0

For this to be true this means they must exist in the form of 
$$e^{\frac {i2\pi k}{3}}=1, for ~k=0,1,2$$, there can be an additional phase angle to define all the possible basis
in 2-D

nincompoop · Answer

4 huh? ... hmm so we can use the 4th akin to time in relativity

dan815 · Answer

i have a feeling its always in a tetra hedral shape, but im not sure how to show that and i wonder if i can get a generalization for higher dimensions then

dan815 · Answer

|dw:1429368503186:dw|