pset2[1] - 18.02 Problem Set 2 Due Thursday February 26 at...

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18.02 Problem Set 2 Due Thursday, February 26 at 1:00 PM in 2-106 Reading The material for this problem set is covered in sections TA and LS of the 18.02 Notes, Exercises and Solutions , and sections 17.1, 17.2, 17.4, 19.2, 19.3, 19.7 of Simmons, Calculus with Analytic Geometry, 2nd Edition . Part A (10 points) Exercises from the Supplementary Notes and Exercises (20 problems, 1/2 point each): (1I) : 1I-1, 1I-2, 1I-3, 1I-5 (1J) : 1J-1, 1J-4, 1J-7, 1J-9 (2A) : 2A-1, 2A-2, 2A-3, 2A-4, 2A-5 (2B) : 2B-1, 2B-2, 2B-3, 2B-5, 2B-9 (2G) : 2G-1(c), 2G-4 Part B (25 points) 1. (5 points) Consider the four points A = (1 , 1 , - 1), B = (0 , 1 , 1), C = (1 , - 1 , 0), and D = ( - 2 , 0 , 3). Find the distance between the lines ( AB ) and ( CD ), that is, the distance between the closest points on these two lines, using two different methods: (a) Find a pair of planes that are parallel to both lines, with the first plane containing the line ( AB ) and the second containing the line ( CD ). Then find the distance between these two planes. (b) Find parametric equations of the lines ( AB ) and ( CD ), and find the times at which
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