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Paper 2 – Areas and Volumes
Example
The vector equations of the lines L
1
and L
2 are
�1� � 2 � � 9 � � 4 � � � � � � � � � r � 3 � t �4
and r � �7 � s �2 �7� � 3 � � � � � � 12 � � �1�
� � � � respectively . Let A and B be the points on L
1
and L
2 with parameters t � 0 and s � 0 respectively .
L
1
and L
2 intersect at C .
( a ) ( i ) Find the value of s , the parameter value at C .
( ii ) Hence , find the coordinates of C .
( b ) Let � be the acute angle between L
1
and L
2
. Show that
( c ) ( i ) Write down CA � .
13 cos� � .
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( ii ) Write down CB � .
( iii ) Hence , find the area of the triangle ABC .
The coordinates of the point D are ( �7 , �15 , � 2 ) .
[ 5 ]
( d ) Find the vector equation of the line L
3 that passes the point D and is parallel to
� �
CA� CB .
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