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

[list][br][*]Look at the triangle AFB. Try to express the line [color=#1551b5]a[/color] with [color=#d69210][math]\|\vec u\|[/math][/color] and [color=#0a971e][math]\alpha[/math][/color] (use trigonometry)![br][*]You see that [color=#1551b5]a[/color] is eqal to the x-component of [color=#d69210][math]\vec u[/math][/color] and [color=#b20ea8][math]\|\vec v\|[/math][/color] is equal to the x-component of [color=#b20ea8][math]\vec v[/math][/color]. Now you can express the dot-product with [color=#d69210][math]\|\vec u\|[/math][/color], [color=#b20ea8][math]\|\vec v\|[/math][/color]and [color=#0a971e][math]\alpha[/math][/color]. (notice that the y-component of [color=#b20ea8][math]\vec v[/math][/color] is 0)[br][*]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)[br][*]Is your relation also right when you move point C?[br][*]How could you calculate the lenght of line [color=#1551b5]a[/color] without using the angle [color=#0a971e][math]\alpha[/math][/color][br][/list]