� 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 �
� Properties of the vector product u� v of angle between u and v :
�u1
� � � u � u2 and
�u
� � 3 �
1 . |
�u2v3
� u3v2
�
�
� u� v
� u
ˆ 3v1
� u1v3
� u v sin�n
, where nˆ //( u� v
)
�u1v2
� u2v
�
�
1
�
|
2 . |
i�i � j� j � k
�k
�
0
|
3 . i�j �k , j�k �i and k �i � j 4 . j�i � �k , k � j � �i and i�k
� �j
5 . u and v are parallel if u�v
�0 6 . u and v are perpendicular if u�v � u v 7 . u� v � �( v�u
)
�v1
� � � v � v2 where � is the
�v
� � 3 �
� The area of the parallelogram with adjacent sides AB � and AD � is AB� AD
�
�
� The area of the triangle with adjacent sides AB � and AD � is 1 AB� AD
2
�
�
� The volume of the parallelepiped formed by AB � , AD � and AF �
� � �
� � �AB�AD
��AF � � is www . seprodstore . com
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