Question 9.1.2: Graph the curve traced by the vector function r(t) = 2costi ......

The parametric equations of this curve are x=2 \cos t, y=2 \sin t, z=3. As in Example 1, we see that a point on the curve must also lie on the cylinder x^{2}+y^{2}=4. However, since the z-coordinate of any point bas the constant value z=3, the vector function \mathrm{r}(t) traces out a circle 3 units above the x y-plane. See FIGURE 9.13.