Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics
16 Vectors
� Terminologies of vectors :
AB �
: Vector of length AB with initial point A and terminal point B
OP �
: Position vector of P , where O is the origin
AB �
vˆ �
: Magnitude ( length ) of AB � 1 v v
0 : Zero vector
: Unit vector parallel to v , with v ˆ �1
i : Unit vector along the positive x -axis j : Unit vector along the positive y -axis k : Unit vector along the positive z -axis
� A vector v can be expressed as v � v1i � v2j � v3k or
�v1
� � �
v � v2 �v
� � 3 �
� Properties of vectors :
� � �
1 . AB �OB� OA
2 .
� u1 � � v1 � � u1 � v1
� � � � � � � u � v � u � v
2 2 2 2
�u � �
3 v � �
3 u3 v � � � � � � �
3 � 3 . v and kv are in the same direction if k � 0 4 . v and kv are in opposite direction if k � 0
5 .
� v1� � kv1� � � � � k v � kv
2 2
� v � �
3 kv � � � � 3�
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