MATH 21A Midterm: MATH 21A Harvard 21a Fall 14Practice1
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Tth 11:30 jameel al-aidroos: start by printing your name in the above box and check your section in the box to the left, do not detach pages from this exam packet or unstaple the packet, please write neatly. Answers which are illeg- ible for the grader cannot be given credit: show your work. Problem 1) (20 points) no justi cations are needed. The vector h0, 6/10, 8/10i is a direction = unit vector. Two nonzero vectors ~v and ~w are perpendicular if ~v ~w = ~0. For any vectors ~u and ~v, we must have ~v proj~u~v = ~u proj~v~u. The plane parametrized by ~r(t, s) = ht, s, 1i is the same as z = 1. The surface x2 + y2 2y z2 = 0 is a cone. The curvature of the helix ~r(t) = hcos(t), sin(t), ti at any t is less than 1.
