Let r(t) = (3 cos t, 5 sin t, 4 cos t). Show that r(t) is constant and conclude, using Example 7, that r(t) and r(t) are orthogonal. Then compute r(t) and verify directly that r' (t) is orthogonal to r(t).

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EXAMPLE 7 Orthogonality of r and r' when r Has Constant Length Prove that if r(1) and r' (1) are nonzero and r(t) has constant length, then r(t) is orthogonal to r' (1).