The applet below shows the subtraction of two vectors. You can move around the points, and then use the sliders to create the difference. For question 2, push "Combine Initial" to have the two vectors start at the same place. Answer the questions, and move around the points to check various cases, until you are convinced of the property.

Question 1: Explain in your own words, how to subtract vectors.
Since vectors can be freely moved, we will move them to start at the same position (to make it easier to visualize). To do this, push the "Combine Initial" button, and check "Show Both" to see both at the same time. Then, answer question 5.
Question 2: Is vector subtraction associative? Is this the same as real numbers?
Question 3: What is the relationship between the vector and ?