(a) Show that the path x(t) = (cos t, cos t sin t, sin2 t) lies on a unit sphere.
(b) Verify that x(t) is always perpendicular to the velocity vector v(t).
(c) Use Proposition 1.7 to show that if a differentiable path lies on a sphere centered at the origin, then its position vector is always perpendicular to its velocity vector.
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