Chapter 11.5, Problem 71E

Closed plane curves Consider the curve r(t) = (a cos t + b sin t)i + (c cos t + d sin t)j + (e cos t + f sin t)k, where a, b, c, d, e, and f are real numbers. It can be shown that this curve lies in a plane.

71. Graph the following curve and describe it.

$\begin{array}{c}r(t)=\left(\frac{1}{\sqrt{2}}\cos t+\frac{1}{\sqrt{3}}\sin t\right)i+\left(-\frac{1}{\sqrt{2}}\cos t+\frac{1}{\sqrt{3}}\sin t\right)j\\ +\left(\frac{1}{\sqrt{3}}\sin t\right)k\end{array}$