What does the dot product of two vectors represent? I know how to calculate the dot product of two vectors alright. However, it is not clear to me what, exactly, does the dot product represent.
The product of two numbers, $2$ and $3$, we say that it is $2$ added to itself $3$ times or something like that.
But when it comes to vectors $\vec{a} \cdot \vec{b}$, I'm not sure what to say. "It is $\vec{a}$ added to itself $\vec{b}$ times" which doesn't make much sense to me.

The dot product of two vectors u,v is the area of the parallelogram u,v' where v' is v rotated by 90 degrees.
