MATH 21B Midterm: MATH 21B Harvard 21b Fall 07second Midterm Practice3
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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. There are two unit vectors ~v, ~w for which the sum ~v + ~w has length 1/3. For any three vectors, we have |(~u ~v) ~w| = |(~v ~w) ~u|. Denote by d(p, l) the distance from a point p to a line l in space. For any point p and any two lines l, k in space, we have d(p, l) + d(p, k) d(l, k).
