Chapter 12.1, Problem 47ES

In each part, match the vector equation with one of the accompanying graphs, and explain your reasoning.

$\begin{array}{l}\left(\text{a}\right)\text{r}=t\text{i}-t\text{j}+\sqrt{2-t^{\text{2}}}\text{k}\hfill \\ \left(\text{b}\right)\text{r}=\sin \pi t\text{i}-t\text{j}+t\text{k}\hfill \\ \left(\text{c}\right)\text{r}=\sin t\text{i+}\cos t\text{j}+\sin 2t\text{k}\hfill \\ \left(\text{d}\right)\text{r}=\frac{1}{2}t\text{i}+\cos 3t\text{j}+\sin 3t\text{k}\hfill \end{array}$