Find the radius of curvature of the curve generated by the position vector r (t) = (-40 sin(t),–9t, 40 cos(t)) for any value of t

Q: Find the moving trihedral and the curvature at any point of R(t) = (t²,– cos 8t, sin 8t).

A: Moving trihedral are three unit vectors of curve  Unit tangent vector  Unit normal vector  binomial…

Q: Find the curvature K of the curve. r(t) = 4 cos 2rti + 4 sin 2rtj K =

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Q: Find the length of the curve r = cos(f) + sin(0), 0sOs

A: The objective is to find the length of the curve.

Q: Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) =…

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Q: The position vector of a particle moving along a helix is c(t) = (cos(t), sin(t), t²). (a) Find the…

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Q: (a) Find the curvature and the radius of curvature of the curve r(t) = 3 cos ti +4 sin tj + tk at t…

A: Given r(t) = 3 cost i + 4 sint j + t k

Q: . Find an equation for the circle of curvature of the curver(t) = ti + (sin t)j at the point (pi/2,…

A: The parameterized curve are x = t , y = sin t The derivatives are                           y = sin…

Q: (a) Find the tangent line(s) to the parametric curve given by x(t) = t° – 4t", and y(t) = t. at the…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

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: The curvature of the curve 7(t)=<6t, 6t+1, sin2t) at t= 4 is

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Q: Find the curvature of the curve defined by F (+) = (5 cos(t), 6 sin(t)) at t = 2

A: κ=  r'(t)→× r"(t)→r'(t)→3 We have to just evaluate for given r(t)

Q: Find the curvature of the curve defined by 7(t) = (6 cos(t), 3 sin(t)) at t 6

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Q: Let C be the curve represented by R(t) = (cos 2t, 2√3t, 5 — sin 2t). Determine the curvature of C at…

A: Let us consider the curve r(t)→ The curvature is obtained as κ=r'(t)→xr''(t)→|r'(t)|

Q: Find the arc length traced out by the endpoint of the vector-valued function 7(t) = t cos t î + t…

A: Solved below.

Q: Find the unit tangent vector to the curve at the specified value of the paramet r(t) = 4 cos(t)i + 4…

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Q: 23. Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) =…

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Q: Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0,…

A: The curve is r(t)=a cos3ti + a sin3tj   Interval is 0, 2π

Q: Find the parametric equations of the tangent line LT to the curve C:r (t) = 2 cos(t)i + sin(t)j +…

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Q: Find the curvature of the curve r(t) = 2 cos πti + sin πtj .

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Let C be the curve represented by Ŕ(t) = (cos 2t, 2√3t, 5 — sin 2t). - ㅠ Determine the curvature of…

A: To find out the curvature of C.

Q: Find the slope of the tangent to the parametric curve c(t) = (cos t, sin t) at the point (–1/2,…

A: We need to find the slope of the tangent to the parametric curve c(t)=(cos t, sin t ) at the point…

Q: The curvature of the curve (t) = 6t, 6t+1, sin2t at t= TT 0 1 8. 01 01 18 O 2 1/2

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Q: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

A: First of all, consider the given parametrized equation of curve C. Rearrange the equations to write…

Q: Find the curvature of the curve r(t) = a cos ωti + b sin ωtj .

A: Given vector is r(t)=acos ωti+b sin ωtj . Compute the derivatives. r'(t)=acos ωti+b sin…

Q: Find the radius of curvature of the curve r=t°i+ 2t´j- - tk at the point where t= 1

A: Since you posted multiple question in this question which are not interlinked so i have solved first…

Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

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Q: 4. Find the radius and centre of curvature of the curve x = (1 - at) cos t + a sin t, y = (1 – at)…

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Q: Find the curvature K of the curve. r(t) = 4 cos 2nti + 4 sin 2ntj K.

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Q: Find the unit tangent vector T and the curvature x for the following parameterized curve. r(t) = (5…

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Q: Find the curvature of the curve F(t) = (cos(5t), sin(5t), 3t) at the point t

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Q: The curvature of the curve 7(t)=6t, 6t+1, sin2t) at t= is 4 18 1 8 0 1 1/2 2.

A: we have to find the curvature

Q: Find the unit tangent vector T and the curvature k for the following parameterized curve:

A: the given curve:r(t)=9 cost , 9 sin t ,3tfirstly, differentiate the given functionr'(t)=-9sint , 9…

Q: 1) Calculate the curvature of the position vector F(t) = sin t ax + 2cost ay + V3 sin t āz is a…

A: Formula of Curvature(K) of the position vector r(t):…

Q: 8. Given the vector r(t) = (sint,cos?, In(cos?)), find the equation of the tangent line in…

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Q: Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) =…

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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: Find an equation of the tangent(s) to the curve with parametric equations x = 1 + √t, y = e^(t^2)…

A: Given parametric equation of curve x=1+t   y=et2we want to find equation of tangent at  ( 2, e)

Q: Find the moving trihedral and the curvature at any point of R(t) = (t²,– cos 8t, sin 8t). -

A: Given is : R→(t)=t2,-cos(8t),sin(8t) In order to find the curvature use the formula . Formula for…

Q: Find an equation of the tangent(s) to the curve with parametric equations E = t cos t, y =t sin t nt…

A: follow next step

Q: Find the curvature of the curve 7(t) = (t – sin t, 1 – cos t) at the point t 2 |

A: Curvature = k= ||T'(t)|| / ||r'(t)||

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

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Q: Find T(t) and a set of parametric equations for the tangent line to the helix given by 7(t) = 2…

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Q: 2. Find the curvature of the curve x(t) t = 1. %3D at

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: The position vector in the xy plane is [t2,sin(t)].  What is the distance traveled by the particle…

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Q: Find the length of the parametric curve x = sin-1t,y = In V1– t² for 0 <t<-

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Q: Find an equation for the circle of curvature of the curve r(t) = t i + (sin t)j at the point (pai/2,…

A: The parameterized curve are x = t, y = sin t.The derivatives are,

Q: The position vector of the particle is 1 R = î cos(t) + ĝ sin(t) + k log (0 <t < T/2). sin t' (a)…

A: Differentiate the position vector R→=costi^+sintj^+log1sintk^ with respect to t, to obtain the…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.