Analysis and Approaches for IBDP Maths Ebook 2 | Page 89

SUMMARY POINTs
�
Intersections of two lines:
1. Intersect at one point (One intersection)
2. Skew (No intersection)
3. Parallel (No intersection)
4. Coincide (Infinite number of intersections)
� Forms of the plane with fixed point A( a1, a2, a
3)
and normal vector
1.
2.
� x � � n1 � � a1 � � n1
�
� � � � � � � �
y � n � a � n
2 2 2
� z � � n � �
3
a � �
3
n �
� � � � � � � 3 �
2
� z� � a �
� � � 3 �
�n1
�
� �
n � n2
:
�n
�
� 3 �
� x� � a1
�
� � � �
y � a � �u�
�v, � , � � , where u and v are two non-parallel
vectors on the plane
3. n1 x � n2 y � n3z � a1n 1
� a2n2 � a3n3
: Cartesian form
8
�
Intersections of two planes:
1. Intersect at one line
2. Parallel (No intersection)
3. Coincide (Infinite number of intersections)
Solutions of Chapter 8
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79