Your Practice Set – Applications and Interpretation for IBDP Mathematics
3 . The vector equations of the lines L
1
and L
2 are respectively . L
1
and L
2 intersect at P .
�14� � �5�
� � � � r � 18 � t �6 and
� 8 � � �2�
� � � �
� �6 � �1�
� � � � r � �14 � s 2 � �6 � �1�
� � � �
( a ) ( i ) Show that t � 2, where t is the parameter value at P .
( ii ) Hence , find the coordinates of P .
R ( a , 4 , 3 ) is a point lying on L
2
.
[ 5 ]
( b ) Write down the value of a . [ 1 ]
�
Q is a point on L
1 such that RQ � � 4 i � 4 j�k .
( c ) ( i ) Write down OR � .
( ii ) Hence , find the coordinates of Q .
Let T and S be the points on L
1
and L
2
where PT
� �
�
�
� 6 PQ and PS � 14PR .
[ 3 ]
( d ) Write down
( i ) PQ � ;
( ii ) PT � ;
( iii ) PR � ;
( iv ) PS � .
( v ) Hence , find the exact area of the quadrilateral QRST . [ 8 ]
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