Analysis and Approaches for IBDP Maths Ebook 2 | Page 91

�5� � �4k
�
� � � �
2. Consider the lines L
1
and L
2
defined by L1
: r �
5
�s k
and L2
�3� � 0 �
� � � �
� 3 � � k �
� � � �
: r �
2 �t
1
,
�10� � 1�
� � � �
k � . It is given that the angle between L
1
and L
2
is not perpendicular. Find the range
of values of k .
3. Consider the lines L
1
and L
2
defined by L1
�7� � 4 �
�15 � � 6 �
� � � �
� � � �
: r �
5 �s
3
and L2
: r � �8 � t
�5
.
� 0� � �1�
�
� � � �
1 � � 0 �
� � � �
It is given that L
1
and L
2
intersect at P . Find the coordinates of P .
[4]
[5]
4. Consider the lines L
1
and L
2
defined by L1
x � k �y �5 z � 4
: � � and
3 4 � 3
� 5�
�1�
� � � �
L2
: r �
3 �t
2
, k � . It is given that L
1
and L
2
intersect. Find the value of k .
� 2�
�1�
� � � �
[5]
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