Below, shows two lines, created with vectors. You can adjust the position vectors (a) and the direction vectors (b), by moving the red circles. The angle between the lines (acute) and the angle between the direction vectors is also shown.
Play with the application, until you understand what it is showing. Then, answer the questions below.

Question 1: Change the position and direction vectors. When vectors affect the angle between the lines?
Question 2: For lines, we are considering the acute angle. What is the relationship between the angle between the lines, and the angle between the direction vectors?
Question 3: Write a formula for , where theta is the angle between the two direction vectors, using the formula for the dot product.
Question 4: Can you create a formula for , where theta is the acute angle between the two lines, using question 2 and 3?