Consider the helix r(t) = (cos(-3t), sin(-3t), -4t). Compute, at t = : A. The unit tangent vector T = ( B. The unit normal vector N = ( C. The unit binormal vector B = ( D. The curvature K =

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Q: 2. Complete all parts: (a) Find the equation of the curve of intersection of the surfaces y = r² and…

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Q: 3) Sketch a graph of the helix r(t) = (− cos(2ñt), 4 sin(2πt), 3t), listing the rotation direction,…

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Q: Consider the parametric curve r(t) = (t³, -t²). Determine which of the following graphs is the…

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Q: П π Find T, N, and k for the plane curve r(t) = 7t i +7 In (cost) j. - <t<2.

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

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A: Given, r(t)=-40sint,-9t,40cost r'(t)=-40cost,-9,-40sint r'(t)=-40cost2+(-9)2+-40sint2=41…

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A: Since you have posted multiple questions. I am answering the first three sub-parts. Please post the…

Q: Solve the equation x" +2x'+2x=25(t-π), x(0)=0, x'(0)=0 a. x(t)==—=sin(2t) x(t)=[1-e-²¹-2te-²¹] +…

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Q: Consider the curve r = (t2,1 – 3t, 1+ t³). (a) Find r'. (b) Does the curve pass through (9, –8, 28)?…

A: To find r'