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 =

Q: Discuss the sub-tangent and sub-normal of a curve at a point. Find the condition that the curves ax2…

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Q: Find an equation for the circle of curvature of the curve r(t) = 8t i + sin(5t) ja

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Q: =urface at the given point. y? at the point (3, 2, 2) 9.

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Q: Consider the following parametric curve. Use the information to answer parts ​(a) and ​(b).…

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Q: Consider the following curve 7(1) = (-2sin(e), –V5,2cos() (a) Find the unit tangent vector. (b) Find…

A: The formula to obtain the unit tangent vector for any curve r(t) is given by: The formula to find…

Q: a. Sketch the surface x2 - y2 + z2 = 4. b. Find a vector normal to the surface at (2, -3, 3). Add…

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Q: The motion of a vibrating particle is defined by the position vector r = (4 sin nti – (cos 2ntj,…

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

A: Given surfaces: y=x2  and   z=x3 a) Rewriting the above equations in parametric form: Let xt=t…

Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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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: The path equation of a particle is given by r = -t²î + cos(2t)ŷ. Find, for t = T/4 s, (а) г, v, а;…

A: Due to guidelines, I'll be solving first three subparts and giving hints to fourth subpart.

Q: Laplace equation will be а. Нурerbolic b. Elliptic c. Parabolic d. Circular

A: Since Laplace equation is  Uxx + Uyy = 0.

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…

Q: 3. Find the 1-parametric equation of the line in the plane passing through the vector P=[]-[9] Hint:…

A: p = [-3,2]q = [0,-3]now find parametric equation lines

Q: (i) = 5. If r(t) = tcostī + tsintī+3tk, Answer each of the following: Find an equation of the…

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Q: Find the radius of curvature of the curve generated by the position vector r (t) = (-40 sin(t),–9t,…

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

Q: A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level…

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] +…

A: Given differential equation

Q: Given the parametric curve r (t)=⟨sin(πt),t⟩ where −1≤t≤1, find r ′ (t) and sketch the curve,…

A: The given curve is, rt=sinπt,t where -1≤t≤1. A tangent vector shows the direction of the motion. The…

Q: a. Find the normal vector to the tangent plane b. Find an equation of the tangent plane to the given…

A: What is Parametric Surface: The concept of parameterized curves is extended to vector-valued…

Q: State the formula to find the Curvature of a curve in parametric form.

A: We will state the required formula.

Q: Find the curvature of the curve r(t) = (-2+5 cost, -1, - 3 - 5 sin t) at the point t = A|CO 3 ㅠ.

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Q: Find the unit tangent vector T(). Fed a set of parametric equations for the line tangent to the…

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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'