Your Practice Set – Applications and Interpretation for IBDP Mathematics
Solution
( a ) |
( i ) |
� x�1�2t � x�9�4s � �
L1 : �y � 3 �
4t
, L2 : �y � � 7 �
2s �
�z � 7 �
3t � � z
�12
�s
|
( M1 ) for valid approach |
|
|
1�
2t �
9�
4s
2t
�8�
4s t
�4�
2s 3�
4t � �7 �
2s �3� 4 ( 4� 2 s) � �7 �
2s
|
( M1 ) for substitution |
|
|
�13 �8s� �7 �
2s
�6�
6s s �� 1
|
A1 |
( ii )
( b ) b1 � 2i � 4j�3k
� x � 9 � 4 ( �1 ) � 5 � �y � � 7 � 2 ( � 1 ) � � 5
( M1 ) for substitution
� � z �12 � ( �1 ) �13 Thus , the coordinates of C are ( 5 , � 5,13 ) . A1
b2 � 4i � 2j�k b �b � b b M1
1 2 1 2 cos�
( 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
[ 5 ]
[ 3 ]
�
( c ) ( i ) CA � � 4 i � 8 j� 6 k A1
�
( ii ) CB � 4 i � 2 j�k A1
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