Question
Use a computer algebra system to graph the vector-valued function and identify the common curve.$$\mathbf{r}(t)=-\frac{1}{2} t^{2} \mathbf{i}+t \mathbf{j}-\frac{\sqrt{3}}{2} t^{2} \mathbf{k}$$
Step 1
The function $\mathbf{r}(t)$ is given by: $$\mathbf{r}(t)=-\frac{1}{2} t^{2} \mathbf{i}+t \mathbf{j}-\frac{\sqrt{3}}{2} t^{2} \mathbf{k}$$ So, we have $x(t) = -\frac{1}{2} t^{2}$, $y(t) = t$, and $z(t) = -\frac{\sqrt{3}}{2} t^{2}$. Show more…
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