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20. [-/0.18 Points] DETAILS SCALCET9 13.1.AE.004. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Example Video Example () Sketch the curve whose vector equation is r(t) = 6 cos(t) i + 6 sin(t) j + 3tk. Solution The parametric equations for this curve are y = 6 sin(t), z = Since x 2 + y? = + 36 sin (t) = , the curve must lie on the circular cylinder x2 + y? = . The point (x, y, z) lies directly above the point (x, y, 0), which moves counterclockwise around the circle x2 + y2 = in the xy-plane. (The projection of the curve onto the xy-plane has vector equation r(t) = (6 cos(t), 6 sin(t), 0). See this example.) Since z = 3t, the curve spirals upward around the cylinder as t increases. The curve, shown in the figure below, is called a helix. 10 , 6 , 3 2 ( 6, 0, 0 )