MATH 230 Midterm: Math 230 SP17Midterm1
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Instructions: please, write your solutions clearly and completely. Answers without work will be given no credit. Spring 2017: (16 points) for this problem, consider the points a(2, 1, 2), b(3, 1, 5), c(0, 0, 1), and d(1, 0, 4). (a) (6 points) calculate the area of the triangle abc. (b) (6 points) calculate comp . Spring 2017: (8 points) find symmetric equations of the line passing through the point (3, 1, 4) which is orthogonal to the plane with equation x + y z = 1. Give the names of these curves. (b) (5 points) match the surface with one of the gures below. Spring 2017: (10 points) find the length of the curve r(t) = (cid:28)2. 3 t3, t + 4, t2 7(cid:29) for t between 1 and 5. Spring 2017: (10 points) calculate the curvature of the curve given by r(t) = (cid:28) e3t. , cos t + sin t, t + 1(cid:29) at the point (cid:18)1.
