Analysis and Approaches for IBDP Maths Ebook 2 | Page 101

s �� 1
� x � 9 � 4( �1) � 5
�
��y
� �7 � 2( �1) � �5
�
� z �12 � ( �1) �13
(M1) for substitution
Thus, the coordinates of C are (5, � 5,13) . A1
(b) b1 � 2i � 4j�3k
(c)
b2 � 4i � 2j�k
1 2 1 2 cos�
A1
b �b
� b b M1
(2i � 4j� 3 k) �(4i � 2 j�k)
� � � � � � � �
2 2 2 2 2 2
( 2 ( 4) 3 )( 4 ( 2) ( 1) )cos�
A1
(2)(4) � ( �4)( �2) � (3)( �1) � ( 29)( 21)cos� A1
13 � 609 cos�
13
cos� � AG
609
The coordinates of A and B are (1, 3, 7) and
(9, � 7,12) respectively. (A1) for correct values
�
CA � ( i � 3 j� 7 k ) � (5 i � 5 j�
13 k )
�
CA � � 4 i � 8 j�
6 k A1
�
CB � (9 i � 7 j� 12 k ) � (5 i � 5 j�
13 k )
�
CB � 4 i � 2 j�k
A1
The area of the triangle ABC
1
� �
� CA � CB
(M1) for valid approach
2
1
� ( � 4 i � 8 j� 6 k ) � (4 i � 2 j�k
)
2
�(8)( �1) � ( �6)( �2)
�
1 �
�
� ( 6)(4) ( 4)( 1)
2
� � � �
� ( �4)( �2) � (8)(4) �
�
�
1
� � 20 i � 28 j�
24 k
2
1 ( 20)
2 ( 28)
2 ( 24)
2
� � � � � � A1
2
[5]
[3]
8
www.seprodstore.com
91