Analysis and Approaches for IBDP Maths Ebook 2

Your Practice Set – Analysis and Approaches for IBDP Mathematics 30 Paper 1 Section B – Areas and Volumes Example The vector equations of the lines L 1 and L 2 are �1� � 2 � � 9 � � 4 � � � � � � � � � r � 3 � t �4 and r � �7 � s �2 �7� � 3 � � � � � � 12 � � �1� � � � � 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) Let � be the acute angle between L 1 and L 2 . Show that (c) Find the exact area of the triangle ABC . The coordinates of the point D are ( �7, �15, � 2) . 13 cos� � . 609 [5] [3] [6] (d) Find the vector equation of the line L 3 that passes the point D and is perpendicular to the plane ABC , giving the answer in parametric form. (e) The perpendicular distance from the plane ABC to D is k 110 of k . . Find the value [2] [8] Solution (a) � 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 90 SE Production Limited

Analysis and Approaches for IBDP Maths Ebook 2 | Page 100