Find the curvature K of the curve represented by rt Report A

Find the curvature K of the curve represented by r(t)=<t,t,1-t^2>??
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r(t)=ti + tj + (1-t^2)k
r\'(t) = i + j - 2tk
r\'\'(t) = -2k
r\'(t) * r\'\'(t) = 2j - 2i
||r\'(t) * r\'\'(t)|| = 2^2 + 2^2 = 22
||r\'(t)|| = 1+1+4t^2 = 4t^2+2
curvature, k = ||r\'(t) * r\'\'(t)||/||r\'(t)||^3
k = 22/(4t^2+2)^3/2
k = 22/22(2t^2+1)^3/2
k = (2t^2+1)^-3/2

$Find the curvature K of the curve represented by r(t)=<t,t,1-t^2>?? Report AbuseSolutionr(t)=ti + tj + (1-t^2)k r\'(t) = i + j - 2tk r\'\'(t) = -2k r\'(t)$

Find the curvature K of the curve represented by rt Report A

Solution

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