Then you should know about the cross product ×, and know what to feed into a four-function calculator to compute it:
If you have memorized the formula in x-y-z coordinates, just change the subscripts from x,y,z to 1,2,3 to convert. The coordinate formulation should look very similar to the coefficients I defined in the paper...in fact, the second part rewrites (in the paper's notation) to
There's some "stratosphere math" that explains how things are defined so this works out. Rather than go into that here, just use the result:
We can rephrase the entire paper to talk about making inferences about coordinates a1..4, b1..4 from the coordinates of the four cross-products
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