Analysis and Approaches for IBDP Maths Ebook 2 | Page 90

Your Practice Set – Analysis and Approaches for IBDP Mathematics
27
Paper 1 Section A – 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]
Exercise 27
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]
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