MATH 0240 Final: MATH 240 Final Exam-41
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Show that the points a (2, 1, 3), b (0, 5, 5), c (3, 6, 9) and. D (5, 2, 7) are the vertices of a parallelogram p and calculate the area of p. L1 : x = t + 2, y = 3t + 1, z = t + 3, l2 : x = 2s + 3, y = 2, z = 4s 2, intersect. If they intersect, nd the point(s) of intersection. The position of a particle at time t is given by the function r(t) = (cid:10) 1. 3 t3, 2t sin t, 2t cos t(cid:11) , t 0. Find the speed v(t) of the particle, the tangential component at (t) of its acceleration and the distance traveled (arc length) between the times t = 0 and t = 3. Let z = xy, x = uv, y = vw. Give your answers in terms of the variables u, v and w alone.
