MAC 2313 Midterm: MAC2313 F00 Test 4
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Name: (1) answer the following, for the vectors: (a) (10 pts. ) Find the vector projection of u along v. u = h1, 2, 3i, v = h2, 2, 1i, w = h 1, 0, 1i (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. (2) (20 pts. ) The position of a moving object is given by (a) find the velocity and acceleration functions v(t), and a(t). r(t) = (cid:173)1 t2, sin(2 t), t3 ; 0 t 1 (b) find the equation of the tangent line ~ (t) = hx(t), y(t), z(t)i to the curve at t = 1. 2 (c) find the net distance traveled by the object. (3) (20 pts. ) Apply the second derivative test to classify each critical point as a relative minimum, relative maximum, or saddle point. f (x, y) = x3 2xy + y2 40y 25x.
