Question

How do I find the orthogonal projection of two vectors?

Answer 1

The question perhaps is about projection of some `vecb` on another `veca` in the same vector space. If this projection is vector `vecp`, then set the vector dot product `veca` and (`vecb`-`vecp`) equal to 0, because `veca` and `vecb`-`vecp` would be orthogonal.

Since `vecp` is along `veca`, it would be some multiple of `veca`. let it be x

Thus `veca. (vecb-xveca)`=0, x= `(veca.vecb)/(|a||a|)`

Hence `vecp`= x `veca` =`(veca.vecb)/(|a||a|) veca`