MATH 0180 Midterm: MATH 180 Brown Exam m180s9b
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Math 180 solution to quiz #9b: cole. Let s be the triangle abc using points a(0, 3, 0), b(1, 2, 1), and c(2, 1, 0). (a) (4 points) construct a parameterization r: d s where d is a region in the uv- plane. Hint: let x = u, y = 3 u, z = v, and let d be a triangle in the uv-plane. Find the vertices of this triangle d. (b) (1 point) find the unit normal n for s with rst component positive. Do n and n (from (a)) point in the same or opposite directions? (c) (5 points) let f = y z, x 3, xyz . Find i = the ux of f through s in the direction of n. hint: use the results of (a) and (b). Solution: (a) following the hint, let r(u, v) = x, y, z = u, 3 u, v .
