1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Find the curvature at a point(vector function)

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the curvature of r(t)= <t^2, lnt, t lnt> at the point P(1,0,0)

    2. Relevant equations
    K(t) = |r'(t) x r''(t)|/(|r'(t)|^3)

    3. The attempt at a solution
    r'(t) = <2t, t^-1, lnt+1>
    r''(t) = <2, -t^-2, t^-1>

    |r'(t) x r''(t)| = sqrt[t^-4(4 + 4 lnt + ln^2t) + (4 ln^2t)]
    |r'(t)| = sqrt[4t^2 + t^-2 + (ln^2t +2 lnt + 1)]

    I don't know what value of (t) to sub into K(t) to get my final answer. I also have a feeling that my cross product is not right. Any help would be much appreciated.
  2. jcsd
  3. Oct 23, 2011 #2


    User Avatar
    Science Advisor

    You want [itex](t^2, ln(t), tln(t))= (1, 0, 0)[/itex].

    What value of t gives you that?

    You are right that your cross product is wrong. Put your value of t into r' and r'' before calculating the cross product. That will simplify it a lot.
  4. Oct 23, 2011 #3
    Thanks a lot HallsofIvy, t = 1 provided I did the rest of the question right.
  5. Oct 23, 2011 #4


    User Avatar
    Science Advisor

    t= 1 whether you did the rest of the problem right or not!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook