Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 35
1 . The vector equations of the lines L
1
and L
2 are
�15� � 6�
� 0 � � �3�
� � � � � � � � r � 11 �t 3
and r � 7 �s 2
� 6 � � 2�
� � � � � �4� � �6�
� � � � respectively . Let A and B be the points on L
1
and L
2 with parameters t � 0 and s � 0 respectively .
L
1
and L
2 intersect at C .
( a ) ( i ) Find the value of t , the parameter value at C .
( ii ) Hence , find the coordinates of C . [ 5 ]
( b ) ( i ) Write down CA � .
( ii ) Write down CB � .
( iii ) Hence , find the area of the triangle ABC . [ 5 ]
( c ) Find the vector equation of the line L
3 that passes the point C and is parallel to
� �
CA� CB .
D is a point on L
3 such that the coordinates of D are ( 73 , � 95 , d) .
[ 2 ]
( d ) Find the value of d . [ 2 ]
( e ) ( i ) Write down CD � .
( ii ) Hence , find the volume of the pyramid ABCD . [ 4 ]
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