Atornado is formed when a tube of air circling a horizontal axis is tilted up vertically by the updraft from a thunderstorm. if t is time, this process can be modeled by the wind velocity field f (t, x, y, z) = (cos t j + sin t k ) × r and 0 ≤ t ≤ π 2 . (a) rewrite f (t, x, y, z) by computing the cross-product. f (t, x, y, z) = ⟨zcos(t)−ysin(t), xsin(t), −xcos(t)⟩ (b) find curl f = ⟨0,2cos(t),2sin(t)⟩ (c) determine the direction of curl f under the following conditions. at t = 0 , curl f is horizontal , and pointing in the direction. for 0 < t < π 2 , curl f is parallel to the -plane, and making an angle of t radians