MATH 21A Study Guide - Midterm Guide: Parametric Equation, Cylindrical Coordinate System, Curve
Document Summary
This space is excluded here in order to save printing resources. Problem 1) tf questions (20 points) no justi cations needed. The length of the sum of two vectors is always the sum of the length of the vectors. For any three vectors, ~v ( ~w + ~u) = ~w ~v + ~u ~v. The set of points which satisfy x2 + 2x + y2 z2 = 0 is a cone. The surface ~r(u, v) = hcos(u2) sin(v2), sin(u2) sin(v2), cos(v2)i with 0 u < 2 , 0 v is a sphere. If p, q, r are 3 di erent points in space that don"t lie in a line, then ~p q ~rq is a vector orthogonal to the plane containing p, q, r. The line ~r(t) = h1 + 2t, 1 + 3t, 1 + 4ti hits the plane 2x + 3y + 4z = 9 at a right angle.
