6 . The coordinates of the points O , A , B , C and D are ( 0 , 0 , 0 ) , ( 0 , 0 , � ) , ( �, 0 , � ) , ( � , 0 , 0 ) and ( 0 , � �, 0 ) respectively . E is a point on the line segment BD such that CE
� BD .
( a ) |
( i ) |
Find the vector equation of BD , giving the answer in the form |
|
|
r
�a
�tb
.
|
( ii ) Express CE � in terms of t .
( iii ) Hence , show that the coordinates of E are
�2 1 2 � � � , � � , � � �3 3 3 � . [ 7 ]
( b ) ( i ) Write down BA � .
Let
�
� w �BA�BD .
( ii ) Find w .
( iii ) Hence , find the acute angle between w and
�1
� � � 1
.
�2� � �
[ 7 ]
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