MAC 2313 Midterm: MAC2313 F96 Test 4
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December 6, 1996: answer the following, for the vectors: u = h2, 2, 3i, v = h3, 2, 1i, w = h 1, 0, 1i (a) (10 pts. ) Find the vector component of u in the direction of v. (b) (15 pts. ) If u, v and w all have their initial points at the origin, nd the general equation of the plane passing through their terminal points: (20 pts. ) F t ds where c is the line segment connecting the point ( 2, 0, 1) to the point (1, 1, 2), and f(x, y, z) = h2x, 0, zi: (20 pts. ) Answer the following for the vector eld f(x, y) = hx xy2, 3 x2yi. (a) show that f is conservative. (b) find a potential function f (x, y) such that f = f. (c) evaluate ic. F t ds where c is any smooth path from (0, 2) to (2, 1): (25 pts. )
