1) Calculate the curvature of the position vector F(t) = sin t ax + 2cost ay + V3 sin t āz is a circle, also find its radius.

Q: 04. Show that the Gauas and mean curvatures on, X-(u+v,u-v, uv) at u=1, v=1 are K=1/16 and H= JI.…

A: Given: 1) X=(u+v,u-v,uv) at u=1,v=1. 2) The paraboloid is xy=aZ.

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Q: 2.Let a be a unit speed curve lying on a sphere center c and radius a > 0. Find the minimum value of…

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Q: Find the curvature of y = sin(3x) at a = 프 4

A: We Know that The curvature measures how fast a curve is changing direction at a given point.

Q: 3. Find the curvature of the plane curve (t, t") at t = 1.

A: see below the answer and calculation as per bertleby guideline I have to solve only 1 question. For…

Q: 1) Calculate the curvature of the position vector r(t) = sin tāx + 2costāy + V3 sin tāz is a circle,…

A:

Q: Find the curvature of the curve r(t). r(t) = (3 + 6 cos 9t) i - (8 + 6 sin 9t)j + 6k Group of…

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Q: TU? TU? r(t) = (/ * du, sin -du ) , t > 0 COS 2 2

A: r(t)=∫0tcosπu22du,∫0tsinπu22du,t>0 We have to find the unit tangent vector T and Curvature K for…

Q: Obtain the curvature of x= k (0 – sin 0); y=k(1+ cos0) in terms of '0'.

A: This is the question from application of advanced Differential Calculus.

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Q: . Sketch the curve parametrized by r(t) = (ltl + t, ltl - t)

A: The given curve is rt=t+t, t-t. Sketch the graph of the above curve as shown below.

Q: at a unit-speed regular parametrised curve 3: (-7, 7)→ R² with T, N) has constant curvature k> 0.…

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Q: In Exercises 1–8, find the curve’s unit tangent vector. Also, find the length of the indicated…

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Q: Find the moving trihedral and the curvature at any point of R(t) = (3t2, sin 2t, cos 2t).

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Q: If r(t) = , then unit tangent is a principal unit normal is a and its curvature is a vector scalar

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Q: Chapter 2 - Exercises 1) Calculate the curvature of the position vector f(t) = sin tāx + %3D 2cos…

A: Position vector is a Euclidean vector that represents the position of a point P in space.

Q: Exercise 7. Show that the curvature of a circle of radius r is , and the curvature of the line is…

A: Show that the curvature of a circle of radius r is 1r and the curvature of the line is zero.

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = sin 2x, x…

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Q: 1) Calculate the curvature of the position vector r(t) = sintāx + 2costāy + V3 sin t āz is a circle,…

A: Given position vector is  r→t=sintax→+2costay→+3sintaz→ Then unit tangent vector is…

Q: A curve has a vector equation r = ti+ 4 sin(t)j + 4 cos(t)k. Find the curvature, K.

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Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: find the points on the surface + z² = 1 that have their tangent plane perpendicular to the vector…

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Q: Find the center of curvature of y = x3 at the point (1, 1) A. (-4, 8/3) C. (6, -2/3) B. (4, -8/3)…

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Q: FInd the curvature of f(t)=ti+t^2j+t^3k at (2,4,8)

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Q: Which type of surface does the curvex= cos(3t),y= sin(3t),z=t, lie on?

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Q: Find the curvature of r(t) = at the point (1,0,0)

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Q: Find the curvature of a superellipse defined by the parametric equations…

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Q: 2. Show that if a : [a, b] → R" is a regular parameterization of a curve then the curvature at α(t)…

A: Let,  is a regular parameterization of a curve To show the curvature at  is

Q: ) Calculate the curvature of the position vector f(t) = sin tāx + 2cos t āy + V3 sin tāz is a…

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Q: 7.) rCt) = (5+,3cot), 3sind), 7.1-> Find the arc length of the curve. 72-) Find the unit tangent and…

A: as per our company guidelines we are supposed to answer ?️only first 3️⃣ sub-parts. Kindly repost…

Q: 8. Find the curvature of the vector-valued function r(t) = at the point t = -1.

A: given function is rt=3t2,-4t,1t find the curvature at t=-1 k=r→'t×r→''tr→'t3

Q: Find k (curvature) and t (torsion) for curve C represented by F(t)=(e^t,-e^t,(2t)^1/2)

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Q: 1) Calculate the curvature of the position vector ŕ(t) = sin t āx+ %3D 2costay + v3 sin t āz is a…

A: To calculate the curvature of the position vector r¯t=sintax¯+2costay¯+3sintaz¯  is a cirlceAlso to…

Q: Show that if M" has constant sectional curvature C then Ricci and scalar curvature of M" are Ric =…

A: We know that from given data: If M has a constant sectional curvature C , k. The Uniqueness of this…

Q: Let r (t,t,t) be a curve in 3-dimensional space having unit tangent and norma V2 vectors u and n.…

A: We will use formula of curvature of a curve to solve it.

Q: Find a plane curve a(s) endowed with a unit-speed prametrization by SE (-0, 0) such that its signed…

A: The curvature of the curve αs is given by: αs=∫s0scos(θ(u))du, ∫s0ssin(θ(u))du-----(1) in which…

Q: Show that the Gauas and mean curvatures on , X = (u + v,u –- v,uv) at u = 1, v = 1 are K = 116 and H…

A: Given, X=u+v,u-v,uv u=1,v=1 , k=116 and H=182 We know that, E=xu,xuF=xu,xvG=xv,xv So, we need to…

Q: Question 3: Compute Gaussian & mean curvature on: r(u, v) =u°cosvi+ u'sinvj+uk

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Q: Show that for a plane curve the torsion T = 0.

A: We have to shown that, For a plane curve the torsion T=0

Q: 1) Calculate the curvature of the position vector F(t) = sin t ax+ 2cos tay + V3 sin tāz is a…

A:

Q: Determine the radius of the curvature of the plane curve given by y In sec x at the || point (0,0).

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Q: Show that the ellipse x = a cos t, y = b sin t, a> b>0, has its largest curvature on its major…

A: The curvature for a parametrized curve c(t) = x(t)i + y(t)j is :

Q: 1) Calculate the curvature of the position vector 7(t) = sin tax + %3D 2cos tay + V3 sin tāz is a…

A: In this question we have to find curvature and radius of curvature.

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

A: