dot-product and angle

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