Scale a Vector

Double a Vector.

Vector has magnitude and direction. [br][br]Double Vector [math]A_2B_2[/math][br]Triple Vector [math]A_3B_3[/math][br]

Copy vector AB to point A_1

Vector has magnitude and direction

Add Vector AB to Vector CD

Use the Parallelogram Law

Question 4.3.1

Using a compass and straightedge, describe how you would construct the fourth vertex of the parallelogram given AB and CD placed at the same starting point.

Question 4.3.2

Prove that AB + CD = CD + AB using the Parallelogram Law.

Def. - Closed Under Addition

A set is closed under addition if adding any two vectors from the set always produces another vector that is also in the set.[br][br]For example, if you add two vectors, the result is always a vector (not a scalar or something else). Vector addition always produces a vector, so we say vectors are closed under addition.

Question 4.3.3

Explain why your proof of AB + CD = CD + AB also shows that vectors are closed under addition.