I’m not the sharpest tool in the shed, but I try to exercise what I got and Processing has been my whetstone.

I recently tried out some vector math, cross product, dot product, etc. with good results after some typos slowed me up. This forum proved helpful again, thanks. What I want to do now is apply something I saw after searching “Inverse of a cross product”. The majority of answers were NO, except for One. A professor from the Polytechnica of Equador gave an answer that was very interesting and explained how it is possible using four-vectors. Here’s his answer:

What I want to do is solve this problem and use Processing to show it. I figure I should start by implementing his answer and proving his numbers, but I cant decipher the notation. It looks simple but…

I already have some functions for dot product, cross product and I think Processing has these too.

Suppose C = A X B. If I already have B and C, I want to derive A. Apparently, this is the holy grail of vector algebra and Diego Saa makes it sound simple.

I still don’t know where to start. The first question I have about the notation is he says A = [a,a] = {0,3,4,7}

with a = (3.4.7). So, that means the other a = 0?

He then says, B = {0,-2,2,-3} , so that would be B = [b,b} ?

Then he shows how to multiply,

A∗B=[a,a]∗[b,b]=[ab+a⋅b,ab−ba+a×b]

If the unbold a and unbold b are zeros, then wouldn’t that be the dot product of a and b is the first element and the cross product of a and b is the other 3 elements?