Solution Found!
Answer: Closed plane curves Consider the curve r (t) = (a
Chapter 13, Problem 53E(choose chapter or problem)
Closed plane curves Consider the curve r(t) = (a cos t+ b sin t)i + (c cost + 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.
Graph the following curve and describe it in words.
\(\begin{aligned} \mathbf{r}(t)=&\left(\frac{1}{\sqrt{2}} \cos t+\frac{1}{\sqrt{3}} \sin t\right) \mathbf{i}+\left(-\frac{1}{\sqrt{2}} \cos t\right.\\ &\left.+\frac{1}{\sqrt{3}} \sin t\right) \mathbf{j}+\left(\frac{1}{\sqrt{3}} \sin t\right) \mathbf{k} \end{aligned} \)
Questions & Answers
QUESTION:
Closed plane curves Consider the curve r(t) = (a cos t+ b sin t)i + (c cost + 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.
Graph the following curve and describe it in words.
\(\begin{aligned} \mathbf{r}(t)=&\left(\frac{1}{\sqrt{2}} \cos t+\frac{1}{\sqrt{3}} \sin t\right) \mathbf{i}+\left(-\frac{1}{\sqrt{2}} \cos t\right.\\ &\left.+\frac{1}{\sqrt{3}} \sin t\right) \mathbf{j}+\left(\frac{1}{\sqrt{3}} \sin t\right) \mathbf{k} \end{aligned} \)
ANSWER:Solution 53E
We have to graph the following curve and we have to describe it in words.