bfc793…: “Beyond the quiet number”

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A curve $C$ in space is described by the vector-valued function: $\vec {r}(t) = \vector {2t^2,4t-3,2t}\quad \text {for}\quad -\infty <t<\infty$ Find $t$ such that the curve passes through the point $(2,5,-2)$ , or write DNE if no such $t$ exists. $t= \answer {DNE}$

Find the unit tangent vector to the curve. $\utan (t) = \vector {\answer {4t/\sqrt {20+16t^2}},\answer {4/\sqrt {20+16t^2}},\answer {2/\sqrt {20+16t^2}}}$

Does $\vec {r}$ use arc length of as a parameter?

yes no

Just check to see if $|\vec {r}'(t)| = 1$ .