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I'm not sure what this problem is asking for, I tried taking the derivative of each component, then plugging in t, but the answer gives small equations for each component like x = 1-t. I'm not sure how to reach this answer component. Can someone please explain the entire process clearly? thanks, the other online solutions seem confusing.

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Well, one simple parametrization is $\textbf{r}(t_0) + t \textbf{r}'(t_0)$ where $t \in \mathbb{R}$. Convince yourself by using vector geometry with this picture in mind,

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  • $\begingroup$ I'm sorry, maybe its because I forgot something while reading the last two sections but I can't see what I'm supposed to do with this answer to solve the problem $\endgroup$ – 2316354654 Sep 29 '17 at 1:21
  • $\begingroup$ Just extract the parametric equations from the vector parametrization of the line that I just gave you. Simply put all that information into a vector with three components and just read off those components. $\endgroup$ – Faraad Armwood Sep 29 '17 at 1:50
  • $\begingroup$ alright, so i tried to take the derivative of r(t) to get <-e^-t * sint - cost * e^-t, e^-t * cost - sint * e^-t, -e^-t> , then i tried to solve for t by setting each of these components to <1,0,1>, and i took ln 1 = ln(-e^-t) to get t = 0, but when i plug 0 in the other components for t they don't come out as 1 and 0. what am i doing wrong? is this the right process? $\endgroup$ – 2316354654 Sep 29 '17 at 2:25
  • $\begingroup$ wait i see. when i tried setting r(t)=(1,0,1) i did the arithmetic wrong. then this makes t=0 satisfied $\endgroup$ – 2316354654 Sep 29 '17 at 2:32

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