Analysis and Approaches for IBDP Maths Ebook 2 | Page 87

SUMMARY POINTs
�
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 �
8
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