Your Practice Paper – Applications and Interpretation HL for IBDP Mathematics
� 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�
� Properties of the scalar product uv � of
angle between u and v : 1 . u� v � u1v 1
�u2v2 �u3v3 � u v cos� 2 . i�i � j� j � k �k
�1
3 . i� j � j�k � k �i � 0
�u1
� � � u � u2 and
�u
� � 3 �
4 . u and v are in the same direction if u�v
� 5 . u and v are in opposite direction if u� v � � 6 . u and v are perpendicular if uv � �0 7 . u� v � v�u
8 . u�u
� u
2 u v u v
�v1
� � � v � v2 where � is the
�v
� � 3 �
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