MATH 21A Midterm: MATH 21A Harvard 21a Fall 17Midterm 1
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. The velocity vector of ~r(t) = ht, t, ti at time t = 2 is twice the velocity vector at time t = 1. The curvature of the curve ~r(t) = h2t, 2t, 2ti is always 1/2. If ~u ~v = ~0, then proj~u(~v) proj~v(~u) = ~0. If ~u ~v = ~v ~w, then ~v (~u ~w) = 0. There is a point not at the origin with cartesian coordinates (x, y, z) = (a, b, c) and spherical coordinates ( , , ) = (a, b, c). The two planes 2x + 2y z = 4 and 4x 4y + 2z = 3 intersect in a line. If the distance between two points p and q is zero, then p = q.
