MAC 2147 Lecture 1: KIC Document 0044

d / dt [(3t2i + -2t -1k) (cos t i + sin 2t j - 6 tk)] d / dt [(3t2i + -2t -1k) (cos t i + sin 2t j - 6tk)

A circular cylinder of radius 1 and the hyperbolic paraboloid z = x2 - y2 intersect as shown in Which vector function r(t) = x(t)i + y(t)j + z(t)k has the curve of intersection as its graph if x(0) = 1? r(t) = (cos t)i + (sin t)j + (cos 2t + 1)k r (t) = (cos t)i + (sin t)j + (cos 2t)k r (t) = (sin t)i + (cos t)j + (cos 2t + 1)k r(t) = (sin t)i + (cos t)j + (cos 2t)k r (t) = (sin t)i + (cos t)j + (cos 2t - 1)k r (t) = (cos t)i + (sin t)j + (cos 2t - 1)k

Given that the acceleration vector is a (t) = (-4 cos(-2t)) i + (-4 sin (-2t)) j + (-4t)k, the initial velocity is v (0) = i + k, and the initial position vector is r (0) = i + j + k, compute: The velocity vector v (t) = i+ j+ k The position vector r (t) = i+ j+ k