In this worksheet you will see how the dot-product is related to the angle between two vectors.

Look at the triangle AFB. Try to express the line a with and (use trigonometry)!

You see that a is eqal to the x-component of and is equal to the x-component of . Now you can express the dot-product with , and . (notice that the y-component of is 0)

Proof what you found out in a few examples (Move around Point B) by comparing your result with the dot-product calculated above! (The results might not be exactly equal)

Is your relation also right when you move point C?

How could you calculate the lenght of line a without using the angle