Ok, I got it now. But, the diagram that Bacterius drew invokes my curiosity on this one.

If I were to figure out this one, my life is complete.

FIXED.

Dot product gives you a single scalar value, not a vector, as a result.
Easiest way for me to visualise it is that two normalized vectors pointing in the same direction give 1.0, pointing in opposite directions gives -1.0, and pointing parallel gives 0.0. When calculating the dot of two normalized vectors, the result is a fraction of "how much the same" are these.
It's also used to 'project' one vector onto another -- e.g. how big is B in the A-direction.

Ok, I got it now. But, the diagram that Bacterius drew invokes my curiosity on this one. I know that a dot product is a scalar. If we are to draw the scalar, how long would the scalar be, if we use the same unit of measurement for all vectors A, and B, along with the scalar.

A scalar is just a length, so you can represent it as a line in any direction (as a scalar has no direction) to scale with the length of other vectors in my diagram (so if vector V was 4 units long, then a scalar of 2 would be represented by a line 2 units long, in an arbitrary direction). It was just convenient to align the dot product's value next to the normal vector to make the diagram more readable.

Ok, thanks! Everything is complete now.