5 . The vector equations of the lines L
1 and L
2 are
� 3� � 2 � � � � � r � 6 � t �6 and
�9� � �2�
� � � �
� 1 � � 3 � � � � � r � �2 � s �2 respectively . Let A and B be the points on L
1 and L
2 with
� 3 � � 1 �
� � � � parameters t � 5 and s � 5 respectively .
( a ) Show that the coordinates of C , the point of intersection of L
1 and L
2
, are ( 7 , � 6 , 5 ) . [ 4 ]
( b ) Find the acute angle between L
2 and the z -axis, giving the answer in radians .
( c ) ( i ) Write down CA � .
[ 3 ]
( ii ) Write down CB � .
( iii ) Hence , find the area of the triangle ABC .
D is a point such that BD � CA .
�
( d ) Write down the area of the quadrilateral BDAC .
�
[ 5 ]
[ 1 ]
© SE Production Limited 18 All Rights Reserved 2021