Chapter 12.1, Problem 1QCE

(a)

To determine

The parametric equations, $x=\frac{1}{t}$ , $y=\sqrt{t}$ , and $z={\sin }^{-1}t$ , as a single vector equation of the form, $r=x\left(t\right)i+y\left(t\right)j+z\left(t\right)k$ .

(b)

To determine

To fill: The blank provided in the statement, “The vector equation in part (a) defines $r=r\left(t\right)$ as a vector valued function. The domain of $r\left(t\right)$ is $\underset{¯}{}$ and, $r\left(\frac{1}{2}\right)=\underset{¯}{}$ â€�.