MATH 21A Midterm: MATH 21A Harvard 21a Fall 17Practice1
Document Summary
Answers which are illeg- ible for the grader cannot be given credit: show your work. Problem 1) (20 points) no justi cations are needed. If |~r (t)| = 1 for all t, then the curvature satis es (t) = |~r (t)|. Suppose that at the point ~r(t) the unit tangent vector is h0, 1, 0i and the binormal vector is h0, 0, 1i. Then the unit normal vector at the point is h1, 0, 0i. If |~v + ~w|2 = 2~v ~w, then ~v = 2 ~w. The distance between two points p and q is smaller than or equal to | ~op|+ | ~oq|, where o = (0, 0, 0) is the origin. The line ~r(t) = h5 + 2t, 2 + t, 3 + ti is located on the plane x y z = 0. The arc length of a circle with constant curvature 20 is /10.
