The scalar product of two vectors **A** und **B** is defined
as:

Here f_{AB} is the angle
between the vectors. This we can also write as the projection of
**A** onto **B **(which is to say the component of **A
**along** B**), A||B = |A|·cos(f_{AB}), multiplied with the lenght of
vector **B**:

The scalar product is therefore the area that we obtain by
multiplying the length of |B| with the component of **A** parallel
to **B**. This is shown in the above applet. The area is shown in
yellow when the scalar product has a positive value, and in pink when
it is negative.

**Please note:**

This also works the other way around, and we can project **B** on
**A.** We then get:

All three of the formulas given here for the scalar product are identical.

**Hint:**

You can use the mouse to drag the vectors by their head and by their
tails.