2 . The vector equations of the lines L
1
and L
2 are
�8�
� 2�
� � � � r � 8
�t 0 and
�7�
� 0�
� � � �
� 6 � � 1 � � � � � r � �8 � 2 3 � � s� 3 � respectively . Let A and B be the points on L
1
and L
2 with
� 7 � � 0 �
� � � � parameters t �� 1 and s �� 1 respectively .
( a ) Show that the coordinates of C , the point of intersection of L
1
and L
2
, are
( 4 , 8 , 7 ) .
( b ) Find the acute angle between L
2 and the y -axis.
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( c ) ( i ) Write down CA � .
( ii ) Write down CB � , giving the answer in exact values .
( iii ) Hence , find the value of ˆ ACB .
( d ) Find the area of the triangle ABC .
D , E and F are the points such that ABCFED is a prism , where the triangle ABC is congruent to the triangle DEF . It is given that the total surface area of the prism
ABCFED is 2 ( 30 � 3 ) . Let h be the height of the prism ABCFED .
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8
( e ) ( i ) Find the value of h .
( ii ) Hence , find the volume of the prism ABCFED . [ 4 ] www . seprodstore . com
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