7 . In a game , two balls A and B are moving in a three-dimensional space , which can be modelled by a three-dimensional coordinate plane . At the start ��10� � � of the game , A is at ( 5 , 5 , 0 ) and its velocity vector is 10
.
� 0 � � �
( a ) Write down the vector equation for the displacement of A , giving the answer in the form r �a �tb ,
[ 2 ]
After p seconds , A is at ( � 85 , 95 , 0 ).
( b ) Find p .
At the start of the game , B is at ( 0 , 0 , � 50 ) . After 5 seconds , it is at ( � 50 , 50 , 0 ) .
[ 2 ]
( c ) Find the velocity vector of B . [ 2 ]
( d ) Write down the vector equation for the displacement of B , giving the answer in the form r �a �tb ,
[ 2 ]
( e ) Find the shortest distance between A and B . [ 4 ]
( f ) Hence , write down the time when A and B are closest to each other . [ 1 ]
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