Use the result of Exercise 40 to show that x(t) = (cos 2t,−sin 2t, 2 cos t) lies on a sp...

Use the result of Exercise 40 to show that x(t) = (cos 2t,−sin 2t, 2 cos t) lies on a sphere by showing

that (1, 0, 0) lies on every normal plane to x.

40. Let x be a path with x’ ×x”≠ 0 and suppose that there is a point x0 that lies on every normal plane to x. Show

that the image of x lies on a sphere. (See Exercise 38 concerning normal planes to paths.)