Find the curvature of r(t)= <t^2, lnt, t lnt> at the point P(1,0,0)
K(t) = |r'(t) x r''(t)|/(|r'(t)|^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.