MATH 32A Lecture 5: 11.7-12.1

8. Suppose F=F where r = (z, y, z y=sin t, and z=3t with 0

Let F(x, y, z) - xi + yj + zk. Evaluate the integral of F along each of the following paths. (a) c(t) = (3t, 3t, 30, 0 ts 1 (b) c(t)-(2 cos(t), 2 sin(t), 0), 0 s t 67 (c) c(t) = (2 sin(t), 0, 2 cos(t)), 0 t 67 (d) c(t) = (3t2, t, 2t3), -1 t 2

For the given position vectors r(t) compute the tangent velocity vector r (t). If r(t) = (cos 3t, sin 3t) Then r (t) = ( , ) Find r (pi / 2) = ( , )