Math 2210 Problem Set 3 Problem 1 Find a space curve r(t) that is a spiral of radius 2 centered on the x axis. Summary: Math 2210 Problem Set 3 Key Problem 1 Find a space curve r(t) that is a spiral of radius 2 centered on the x axis. Parameterize your spiral so that the derivative of r projected onto i is constant. Solution 1: r(t) = (t, 2Cos(t), 2Sin(t)) To see this is correct note the derivative in direction i is 1 and that the y and z coordinates make a circle of radius 2. Problem 2 Give the type (e.g. "circle") for each of the following space curves. (i) r(t) = (t2 , 2t + 1, t - 5), (ii) s(t) = (1, 2Sin(t), 5Cos(t)), (iii) t(t) = (0, 5Sin(t), 5Cos(t)), and (iv) u(t) = (5t - 1, Cos(t), Sin(t))). Solution 2: (i) A parabola. (ii) An ellipse of eccentricity 2.5 with its major axis parallel to the z axis, its minor axis parallel to the y axis, and in a plane parallel to the yz-plane with x = 1. (iii) A circle of radius 5 in the yz-plane centered at the origin. (iv) A spiral of radius 1 centered on the x-axis. Problem 3 At what time t does r(t) = (1, t, t2 ) intersect x + y + z - 6 = 0? Collections: Mathematics