Vector Addition
The applet below shows the addition of two vectors. You can move around the points, and then use the sliders to create the sum. For question 5, 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 add vectors geometrically. Note: be specific in your answer.
Question 2: For normal number addition, we have a special number "0", where . Can you create a zero vector 0 such that for any vector ? Describe the properties of this zero vector.
Question 3: For normal numbers , we have a "negative number" where . Choose any vector and then create its negative (satisfying the property above). Repeat this for multiple vectors. Hence, describe how to find a negative of a vector.
Question 4: Consider two vectors and . Describe how to subtract the vectors (finding ).
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 5: Is vector addition associative? Hint: Associative means . Is this the same as real numbers?