Question
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The vector-valued function $\mathbf{r}(t)=t^{2} \mathbf{i}+t \sin t \mathbf{j}+t \cos t \mathbf{k}$ lies on the paraboloid $x=y^{2}+z^{2}$.
Step 1
Step 1: First, we need to express the equation of the paraboloid $x=y^{2}+z^{2}$ in terms of the vector-valued function $\mathbf{r}(t)=t^{2} \mathbf{i}+t \sin t \mathbf{j}+t \cos t \mathbf{k}$. Show more…
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