4 . The coordinates of the points O , A , B , C and D are ( 0 , 0 , 0 ) , ( 3 , 0 , 0 ) , ( 3 , 0 , 3 ) , ( 0 , 0 , 3 ) and ( 0 , � 3 , 0 ) respectively . E is a point on the line segment BD such that AE
� BD .
( a ) ( i ) Find the vector equation of BD , giving the answer in the form r �a �tb .
( ii ) Express AE � in terms of t .
( iii ) Hence , show that the coordinates of E are ( 2 , � 1 , 2 ) . [ 7 ]
( b ) ( i ) Write down BA � and BC � .
� �
Let n
1
�BA�BD
and n
2
�BC�BD .
� �
( ii ) Find n
1
.
( iii ) Find n
2
.
( iv ) Hence , find the acute angle between n
1
and n
2
.
F is a point on the y -axis such that the volume of the pyramid OABCF is 15 .
[ 9 ]
8
( c ) Find the possible coordinates of F . [ 4 ] www . seprodstore . com
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