Your Practice Set – Applications and Interpretation for IBDP Mathematics
33
Paper 1 – Components of Vectors
Example
The vectors a and b are given as
�1�
� � a � 3 and
�6�
� �
� 2 � � � b �
�4
.
��5�
� �
( a ) Write down 2a�
b .
( b ) Hence , find the component of 2a�
b parallel to a .
[ 1 ]
[ 3 ]
Solution
( a ) |
�4�
� � 2a�b �
2 �7�
� �
|
A1 |
( b ) |
The required component |
|
|
( 2 a
�b)
�a
� a
|
( M1 ) for valid approach |
|
( 4 )( 1 ) �( 2 )( 3 ) �( 7 )( 6 )
� 2 2
2 1 �3
�6
|
( A1 ) for substitution |
|
�
7.66698172
|
|
|
�
7.67
|
A1 |
[ 1 ]
[ 3 ]
Exercise 33
1 . The vectors a and b are given as
�5�
� � a � 3 and
�0�
� �
�0�
� � b � 3
.
�0�
� �
( a ) Write down a� 3b .
( b ) Hence , find the component of b parallel to a� 3b .
[ 1 ]
[ 3 ]
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