31
Paper 1 – Intersection Between Lines
Example
Consider the lines L
1
and L
2 defined by L1
�1� � k � � � � �
: r � 3 � s �3 and
�5� � k � 2�
� � � �
� 2 � � k � 2�
� � � �
L2
: r � 0 �t 2 , k � . It is given that L
1
and L
2 are perpendicular . Find the
� �9� � �1
� � � � � possible values of k . [ 4 ]
Solution
L
1
and L
2 are perpendicular .
|
� k � � k�
2� � � �
� � �3 � 2 �
0 � k �2� �
�1
� � � �
�
|
( M1 ) for setting equation |
|
( k)( k � 2 ) � ( �3 )( 2 ) � ( k � 2 )( �1 ) �
0
|
( A1 ) for correct approach |
2 k k k � 2 �6� � 2 � 0
2 k �3k� 4 � 0 ( k�1 )( k� 4 ) � 0 k �� 1 or k � 4
A2 [ 4 ]
8
Exercise 31
1 . Consider the lines L
1
and L
2 defined by L1
� 3 � � k �1�
� � � � : r � �1 � s 20 and
� �2� � �10
� � � � �
� 0� � k � 2�
� � � �
L2
: r � 0 � t k � 2 , k � . It is given that L
1
and L
2 are perpendicular . Find the
� 4� � k � � � � �
possible values of k . [ 4 ] www . seprodstore . com
103