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Thread: curvature k(t) of the curve

  1. January 28th 2009, 05:10 PM #1
    viet
    viet is offline
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    curvature k(t) of the curve

    Find the curvature k(t) of the curve X(t)= (-2 sin t) I + (-2 sin t)J + (1 cos t)K
    k=\frac{|r' X r''|}{|r'|^3}

    r(t) = (-2 sin t) I + (-2 sin t)J + (1 cos t)K

    r'(t) = (-2 cos t) I + (-2 cos t)J + (- sin t)K

    r''(t) = (2 sin t) I + (2 sin t)J + (-cos t)K

    Need help with the cross product, i'm not sure if im doing the cross product right but its:

    r' X r'' = (2 cos^2t)I - (2 cos^2t - 2 sin^2t) + (-4 cos t *sint -4 cos t *sin t)
    Last edited by viet; January 29th 2009 at 07:09 AM.
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