Analysis and Approaches for IBDP Maths Ebook 2 | Page 102

Your Practice Set – Analysis and Approaches for IBDP Mathematics
1 ( 4)
2 (5
2 7
2 6
2 )
� � � �
2
1
� (4 110)
2
� 2 110
A1
(d) The vector equation of the line L
3
:
� �7 � � �20�
� � � �
r � �15 � u
�28
(A1) for correct values
� �2 � � �24�
� � � �
� x� �7 � 20u
�
�y
� � 15 � 28u
�
� z � �2 � 24u
(e) The Cartesian equation of the plane ABC :
( xi � yj � zk) �( �20i � 28j�
24 k)
� ( i �3j� 7 k) �( �20i � 28j�
24 k)
�20x � 28y � 24 z � (1)( �20) � (3)( �28) � (7)( � 24)
�20x � 28y � 24z
� � 272
A1
M1A1
5x � 7y � 6z
� 68
A1
�5( �7 �20 u) � 7( �15 �28 u) � 6( �2 �24 u) � 68 (M1) for substitution
�152 � 440u
� 68
�440u
� 220
1
u �� (A1) for correct value
2
� � 1 �
� x � �7 � 20�� ��
3
� � 2 �
� � 1 �
��y
� �15 � 28�� �� �1
� � 2 �
� � 1 �
� z � �2 � 24�� ��10
� � 2 �
Therefore, the point of intersection of L
3
and ABC
are (3, � 1,10) . A1
2 2 2
� ( �7 �3) � ( �15 � ( �1)) � ( �2 �10) � k 110 (M1) for setting equation
440 � k 110
k � 4
k � 2
A1
[6]
[2]
[8]
92
SE Production Limited