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Calculus and Beyond Homework Help
Need help showing important tangent plane property:
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[QUOTE="ozone, post: 4535332, member: 344731"] Edit: I realized v is just a constant so what we really should have is something like [itex] N = \pm b(t) [/itex]. Also I forgot to mention I had a factor of [itex] |\alpha(t)|^4 [/itex] so that [itex] N = \pm |\alpha(t)|^4 b(t) [/itex] but I assumed that the curve is parameterized by arc-length so that I could ignore this term.. I'm not sure that it should make any difference by including it. Also I should note that I wrote the tangent plane equation down very wrong, it should be given by [itex] T_{t_0,v_0}(S) = N|_{t_0,v_0} \cdot ((x,y,z) - X(t_0,v_0)) [/itex] Which would simplify to [itex] T_{t_0,v_0}(S) = \pm |\alpha(t_0)|^4 (b(t_0) \cdot (x,y,z) - b(t_0) \cdot \alpha(t_0) ) [/itex] Which we would then want to show is not changing as [itex] t_0 [/itex] varies [/QUOTE]
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Calculus and Beyond Homework Help
Need help showing important tangent plane property:
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