Ev(Unit Vector) and projection of a vector in a dot product

[Usernam]

So my book says

Lets suppose,

We have two vector v and u

w=projection of u ev= unit vector θ=angle between the two

w=(u.ev)ev or w=( (u.v)/(v.v) )v

Now, the second equation is fairly easy to understand if we understand the first one because ev= v / |v|

What is bothering me is I have no idea why w=(u.ev)ev.

It would be more reasonable, as per me, if w=(u.ev)

But that is not the case.

Why is that extra ev lingering around in the equation.

ANY IDEAS?

 

[mathman]

w is a vector parallel to ev. (u.ev) is a scalar (± length of w), so you need the entire expression to define the vector w.