MATH 21A Midterm: MATH 21A Harvard 21a Fall 14Midterm 1
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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 surface x2 + y2 + z2 = 1 is a one-sheeted hyperboloid. The equation y = 3x + 2 in space de nes a plane. Whenever |~r (t)| = 1 then | ~t (t)| = 1. The length of the vector projection proj~v( ~w) is smaller than or equal to the length of ~w. The velocity vector of ~r(t) = ht, t, ti at time t = 2 is the same as the velocity vector at t = 1. If ~v ~w = ~w ~v then ~v, ~w are parallel. The vector h 2, 1, 0i is perpendicular to the line h1 + t, 2t, 3ti. The point given in spherical coordinates as = 3, = 0, = is the same point as the point = 3, = 0, = 0.
