Hello, RedKMan!
Are you familiar with "projections"?Let
Decompose the vector into the sum of two orthogonal vectors,
one parallel to , the other orthogonal to
Given vectors
The projection of u onto v is given by: .
. . This is the component of that is parallel to
And: .
. . This is the component of that is orthogonal to
We have: .
. .
. .
Therefore: .