Can you prove the formula for projection of a vector using dot products?

[Bipolarity]

Is the following statement true? My intuition tells me it is true, but I have been trying to prove it, without much success:

$$(proj_{v}u ) \cdot (u - proj_{v}u) = 0$$

It makes complete since if you draw it out in R2, but I am trying to prove it in Rn.

Any ideas?

BiP

 

[micromass]

The formula is true. To prove it, can you find another way to write $proj_vu$?? Try to write it with dot products.