Vector has magnitude and direction. [br][br]Double Vector [math]A_2B_2[/math][br]Triple Vector [math]A_3B_3[/math][br]
Vector has magnitude and direction
Use the Parallelogram Law
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.
(1 mark) Place Vector AB and CD tip to tail from some point P.[br](1 mark) Place Vector CD and AB tip to tail from the same point P.[br](2 marks) Vectors AB + CD and CD+ AB will form the four sides or a parallelogram, with four points as the comers.
Prove that AB + CD = CD + AB using the Parallelogram Law.
(1 mark) Based on the construction it is clear Vectors AB + CD = CD+ AB.[br](1 mark) based on the commutative property of vectors, Vectors AB + CD = CD+ AB.
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.
Explain why your proof of AB + CD = CD + AB also shows that vectors are closed under addition.
(1 mark) States that the diagonal is a vector.[br](2 mark) States that since the sum of two vectors is also a vector, vector addition is closed under addition.