MATH 21A Final: MATH 21A Harvard 21a summer 10Final
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Tth 11:30 sebastian vasey: 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. Except for problems 1-3, we need to see details of your computation: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 180 minutes time to complete your work. For any two nonzero vectors ~v, ~w the vector ((~v ~w) ~v) ~v) is parallel to. The cross product satis es the law (~u ~v) ~w = ~u (~v ~w). If the curvature of a smooth curve ~r(t) in space is de ned and zero for all t, then the curve is part of a line.
