What is the Dot Product of Unit Vectors in Vector Projection?

[teknodude]

I was copying my friends notes and had a hard time understanding one of the examples he had written down from lecture. See the attachment for a the picture of the example. This example looks like a projection of two vectors to me, but I'm not sure.

$$u'=\frac{4i+2j}{\sqrt{20}}$$ u' = unit vector u in the direction of force
$$v'=\frac{3i+4j}{5}$$ v' = unit vector v

$$Fy' = 7kN (\frac{4i+2j}{\sqrt{20}})\cdot (\frac{3i+4j}{5}) = 7kN (\frac{4}{\sqrt{20}} * \frac{3}{5} + \frac{2}{\sqrt{20}} * \frac{4}{5})$$

The unit vectors came from the drawing and are in the direction of the two vectors. The thing i don't get is why are 2 unit vectors being dotted, then multiplied by the magnitude 7 kN?

http://img394.imageshack.us/img394/5998/untitled3bz.png

**EDIT: forgot to include in the image a unit vector symbol in the pic for F, so F = 7 kN e' (e' is a unit vector)

 

[whozum]

It is the same regardless of how you do it. If you multiply out the magnitude of the F vector onto the F's unit vector, you get the original vector F. You can then dot it against the y vector to find [itex] F \cdot y [/tex] (which I think is what your question is asking).

 

[lightgrav]

The subscript on the Fy should be v' instead! (ie, your e' = v')
that is, your notes found the v' component of the 7kN Force
which original vector was along the u' direction.

F_y would be = F cos(phi), where cos(phi) = u'.j (<=dot product)