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.


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,

enter image description here

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.