MAC 2313 Midterm: MAC 2313 FIU Exam 115k
15 Feb 2019
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Line: x = 4 + 2t, y = t, z = 1 4t. Assume u, v etc are arbitrary vectors in r3. If u w = u v and u 6= 0, then v = w. Every plane has exactly two unit normal vectors. projuw = (u w)w/||w||2. If two lines in r3 do not intersect, then they are parallel. If two planes in r3, with normal vectors n1 and n2, do not intersect, then n1 n2 = 0. Every ellipsoid will intersect the z-axis in exactly two points. If u v = 0 then u = 0 or v = 0. r(t) = t2i + t3j is a smooth function. The cross product is independent of the coordinate system: [10 pts] choose one and prove it. Remarks and answers: the average score among the top 20 was approx 66 out of 100, which is a bit low. Most of the problems came from the textbook exercises (see 12. 1. 38,
