Solution r(t) = 6 cos(t) i + 6 sin(t)j + 3tk. The parametric equations for this curve are x= y = 6 sin(t), z = Since x² + y² = + 36.sin²(t) = the curve must lie on the circular cylinder x² + y² = 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.