Analysis and Approaches for IBDP Maths Ebook 2 | Page 103

Exercise 30
1. The vector equations of the lines L
1
and L
2
are
�15� � 6�
� 0 � � �3�
� � � � � � � �
r �
11 �t
3
and r �
7 �s
2
� 6 � � 2�
�
� � � � �4� � �6�
� � � �
respectively. Let A and B be the points on L
1
and L
2
with parameters t � 0 and s � 0
respectively.
(a) Find the coordinates of C , the point of intersection of L
1
and L
2
.
(b) Find the exact area of the triangle ABC .
(c) Find the vector equation of the line L
3
that passes the point C and is
perpendicular to the plane ABC , giving the answer in parametric form.
D is a point on L
3
such that the coordinates of D are (73, � 95, d)
.
[5]
[6]
[2]
(d) Find the value of d .
(e) Hence, find the volume of the pyramid ABCD .
2. The vector equations of the lines L
1
and L
2
are
�8�
� 2�
� � � �
r �
8 �t
0
and
�7�
� 0�
� � � �
� 6 � � 1 �
� � � �
r � �8 � 2 3 � � s� 3 � respectively. Let A and B be the points on L
1
and L
2
with
� 7 � � 0 �
� � � �
parameters t �� 1 and s �� 1 respectively.
[2]
[4]
8
(a) Show that the coordinates of C , the point of intersection of L
1
and L
2
, are
(4, 8, 7) .
(b) Find the angle between L
2
and the y -axis.
(c) Find the value of ˆ ACB.
(d) Find the exact area of the triangle ABC .
[3]
[3]
[6]
[3]
www.seprodstore.com
93