11 . The plane �
1 meets the x , y and z axes at A , B and C respectively . The plane �
2 meets the x , y and z axes at A , B� and C respectively , where B� is the reflection point of B about the x - z plane . The Cartesian equation of the plane �
1 is 8x � 6y �3z
� � 24 .
( a ) Show that the Cartesian equation of the plane �
2 is 8x �6y �3z
� � 24 . [ 6 ]
( b ) Find the volume of the pyramid ABB� C . [ 4 ]
( c ) Find the obtuse angle between �
1 and �
2
. [ 5 ]
( d ) Find the vector equation of the line that passes the mid-point of the line segment BC , and is perpendicular to both �
1 and �
2
, giving the answer in Cartesian form . [ 5 ]
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