11 . The Cartesian equations of the planes �
1 and �
2 are 4x �3y � kz � 24 and 4x �3y � kz � � 24 respectively , k � . The vector equation of the line of
intersection of the planes �
1 and �
2 is given by
�0� � �3� � � � � r � 8 �t
0
.
�0� � 1 � � � � �
( a ) Find k . [ 4 ]
( b ) The plane �
1 meets the x , y and z axes at A ( a , 0 , 0 ) , B ( 0 , b , 0 ) and C ( 0 , 0 , c ) respectively . The plane �
2 meets the x , y and z axes at
A � ( �, 0 , 0 ) , B and C �( 0 , 0 , � c) respectively , where A� is the reflection point of A about the y - z plane .
( i ) Write down the values of a , b , c and � .
( ii ) Hence , find the volume of the pyramid A� ABC .
( c ) ( i ) Find the angle between AC� and the x -axis .
[ 7 ]
( ii ) Hence , find the size of ACˆ
�A� . [ 5 ]
( d ) The line L passing through C is perpendicular to the plane ABC . It is given that the line L meets the plane A�BC� at Q . Find the coordinates of Q , giving the answer correct to four decimal places .
[ 4 ]
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