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Paper 1 – Vector Equations of Lines
Example
The line L
1 passes through the point A ( 3 , 4 , 6 ) and its direction vector is
�1� � � 3 .
�0�
� �
( a ) Write down the vector equation of L
1
.
� k � � �
( b ) The vector v �
�3 is perpendicular to L
1
.
� 7 � � �
[ 2 ]
( i ) Find the value of k .
( ii ) Hence , write down the vector equation of the line passing through A and is parallel to v .
[ 4 ]
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Solution
( a )
� 3� �1�
� � � � r � 4
�t 3 A2
� 6� �0�
� � � �
( b ) ( i ) ( 1 )( k) � ( 3 )( �3 ) � ( 0 )( 7 ) � 0 ( A1 ) for correct equation k �9�
0 k � 9 A1
[ 2 ]
( ii )
� 3� � 9 � � � � � r � 4 � s �3
A2
� 6� � 7 � � � � �
[ 4 ] www . seprodstore . com
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