Projection of one vector on another?

[Joza]

Projection of one vector on another??

Can anyone explain how to find the projection of one vector along another?

I thought it was scalar (dot) product, but then I realized it WASN'T. What is this then?

Anyone explain?

 

[Diffy]

does this site help?
http://www.math.oregonstate.edu/hom...usQuestStudyGuides/vcalc/dotprod/dotprod.html

 

[EnumaElish]

projection of y onto x = x(x'x)^-1x'y [= predicted value of y from the least squares equation "y = a + bx + u"].

 

[HallsofIvy]

The LENGTH of the projection of one vector onto another is (almost) the dot product.

To find the projection of \vec{u} on \vec{v}, draw the line from the "tip" of \vec{u} perpendicular with \vec{v}. You now have a right triangle with angle \theta between the angles and hypotenuse of length |\vec{u}|. The length of the projection, the "near side", is then |\vec{u}|cos(\theta). Since the dot product can be defined as \vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}|cos(\theta), to get the length of the pojection, we need to get rid of that |\vec{v}| by dividing by it. The length of the projection of \vec{u} on \vec{v} is
\frac{\vec{u}\cdot\vec{v}}{|\vec{v}|}

In order to get the projection vector itself, we need to multiply that length by the unit vector in the direction of \vec{v}, which is, of course, \vec{v}/|\vec{v}|.
The vector projection of \vec{u} on \vec{v} is
\frac{\vec{u}\cdot\vec{v}}{|\vec{v}|^2}\vec{v}