1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

2 questions on vector functions

  1. Jul 5, 2008 #1
    1. The problem statement, all variables and given/known data
    1) Find parametric equations for the line that is tangent to r(t) = (sin t)i + (t^2 - cos t)j + (e^t)k at the parameter value t = 0.

    2) For the equation r(t) = (cos t)i + (sin t)j and for t >= 0, is the particle's acceleration vector always orthogonal to its velocity vector?


    2. Relevant equations



    3. The attempt at a solution
    1) According to my text the tangent line to the curve r(t) = f(t)i + g(t)j + h(t)k is the line that passes through the point (f(t0), g(t0), h(t0)) parallel to v(t0), where t0 = 0 in this problem.
    I solved the velocity equation v(t) = (cos t)i + (2t + sin t)j + (e^t)k, and v(0) = i + k.
    This is the answer:
    x = t, y = -1, z = 1+t
    I found the point (f(0), g(0), t(0)) = (0, -1, 1), I'm not sure how to find the equation of a line that passes through this point and is parallel to another line? thanks

    2) For this one I just want to make sure, to find where the acceleration vector is orthogonal to its velocity vector I find where their dot products equal 0, right?
     
  2. jcsd
  3. Jul 6, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The equation of a line passing through a point x(0) with instantaneous velocity v(0) (i.e. tangent line) is x(0)+v(0)*t. And yes, orthogonal means dot product zero.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: 2 questions on vector functions
Loading...