I suspected trolling in your question about geometric vectors.
Sides of a triangle and elements of your algebra are different domains. In order to translate results between them one needs to prove this makes sense.
In the article the author only shows that inner product of c by itself equals to sum of inner product squires of a and b, if a and b are orthogonal.
Who told you this has anything to do with lengths of triangle sides?
Sides of a triangle and elements of your algebra are different domains. In order to translate results between them one needs to prove this makes sense.
In the article the author only shows that inner product of c by itself equals to sum of inner product squires of a and b, if a and b are orthogonal.
Who told you this has anything to do with lengths of triangle sides?