Let $\mathbf { r } ( t ) = \langle \cos 2 t , \sin 2 t , 3 \rangle$

Essay

Let . $\mathbf { r } ( t ) = \langle \cos 2 t , \sin 2 t , 3 \rangle$ . Compute the tangent vector $\mathbf { r } ^ { \prime } ( t )$ and show that it is always orthogonal to $\mathbf { r } ( t )$ .