Analysis and Approaches for IBDP Maths Ebook 2 | Page 98

Your Practice Set – Analysis and Approaches for IBDP Mathematics
� � �
(c) OS �OR� RS
M1
� � �
OS �OR�
QP
�s � r �p �q A1
If P , Q and R are collinear, then the area of
PQRS is zero.
� p�q � q�s � s�p � 0
M1
p�q �q�( r �p �q) � ( r �p �q) �p � 0 A1
p�q �q�r �q�p �q�q �r�p �p�p �q�p � 0 M1
p�q �q�r �q�p �0 �r�p � 0 �q�p � 0 A1
p�q � q�r �r�p
� 0
�p�q �q�r �r�p � 0 AG
[6]
Exercise 29
1. p , q and r are three non-zero vectors. It is given that ( p�q) �r � ( q�r)
�p .
(a) Show that 1 [( p � q) �( q � r)] �( r � p) � ( p�q)
�r .
2
p � p i � p j�
p k , q � q1i � q2j�
q3k and r � r1 i � r2 j�
r3k .
Let
1 2 3
[6]
(b) Show that p�( q�r) � ( p�q) r � ( p�r)
q .
(c) Hence, show that p�( q�r) �q�( r�p) �r�( p�q)
� 0 .
[8]
[3]
2. p , q and r are three non-zero vectors such that p �q �r � 0.
(a) Show that p�q � q�r � r�p .
(b) Show that p�q �q�r �r�p � 0 if p�
�q, � � 0 .
[6]
[3]
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