MATH 21A Midterm: MATH 21A Harvard 21a summer 10Practice4
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Name: start by printing your name in the above box, try to answer each question on the same page as the question is asked. If needed, use the back or the next empty page for work: justify your answers. Answers without derivation can not be given credit: do not detach pages from this exam packet or unstaple the packet, please write neatly. Answers which are illegible for the grader can not be given credit: 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 is perpendicular to ~v ~w. 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.
