Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this function? I. Tangent vector is constant at any point. II. Length of tangent vector at any point is constant. III. Tangent vector is (0,2,1) at the point (1,0,0). 4а+b IV. Curvature at a point (a, b, c) is 50 V. Arclength of the curve from a point (a, b, c) to a point (d, e, f) is given by V5dt a. II, III, V O b. I, II, V O . I, II, IV O d. I, II, IV

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Q: Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this…

A: We have to choose correct option We have to find tangent vector ,it's modulus,arc length, curvature

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A: (b) Starting by finding a single vector function that represents the intersections of the surfaces…

Q: Let r(t)=cos 2t i +sin 2t j + tk be a vector function. Which of the followings are true for this…

A: Let's calculate tangent vector: Tangent vector, T(t)=r '(t). Here, r(t)=cos(2t) i + sin(2t) j +t k,…

Q: Let r(t)=cos 2t i +sin 2t j + tk be a vector function. Which of the followings are true for this…

A: Tangent vector:  For a parametric curve r(t) the tangent vector  is  r'(t), that is, derivative of…

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A: Given vector r(t)=t , t2 , 4

Q: Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this…

A:

Q: 3. (a) Given the vector valued function r(t) = 4cos nti + 4 sin ntj + tk. Find the position vector,…

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Q: 5. Consider the vector function F(t) = (9 – - 2t, 4+ 2t, v2t² ) (a) Find the arc length of the curve…

A: Solution is here

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Q: (A) Given the vector function r(t)=( V21,e', e-), the unit normal vector N(t) is of the %3D form:…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: We need to find radius of curvature.

Q: 2. Find the unit tangent vector T(t), principal unit normal vector N(f), and curvature x, for the…

A: Since you have asked multiple questions, we will solve first question for you. If you want other…

Q: 4. Find the unit tangent vector T(t) for the vector function: r(t) = .

A: To find the unit tangent vector.

Q: 3. Let C be the space curve given with the vector valued function R(t) = (1+2 sin(2nt))i+ (In t)J +…

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Q: Consider the Vector function c :Lもっで参せ> a) Find the もこ0 urc leng th of cle) from to b.) Find the…

A: Given: rt=t, t2, 23t3 To Find: a. Arc length of rt from t=0 to t=1.b. Find the curvature at t=1.

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Q: Consider the following vector function. r(t) = (8/2t, est, e-8t) (a) Find the unit tangent and unit…

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Q: 3. (a) Given the vector valued function r(t) = 4 cos zti + 4 sin atj + tk. Find the position vector,…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let r(t)=cos 2t i +sin 2t j + tk be a vector function. Which of the followings are true for this…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 14. Find unit tangent vector to the curve given below when t =1. x = r, y = Z13, z = 21, 12 0. O i-…

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Q: Consider the following vector function. r(t) = 3t, %3D (a) Find the unit tangent and unit normal…

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Q: Let F(t) = (t2 – 1, 2t, 2t2 + 3). a) Find limo K(t). b) What is the point of maximal curvature? c)…

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Q: Find the unit tangent vector at the indicated point of the vector function r(t) = e3tk T(pi/2) = %3D…

A: Here the given vector is  r→(t)=e3t cos(t) i+e3t sin(t) j+e3t kr→(t)=e3t cos(t) , e3t sin(t)  , e3t…

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Q: 5. Find the unit tangent vector, the unit normal vector and the binormal vector to the curve r(t) =…

A: The given vector curve is:  r→(t)=t3,t2,t Given point is: (1, 1, 1). Therefore t = 1. Now the Unit…

Q: Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this…

A: Here, r(t)=cos(2t) i + sin(2t) j + t k, so, we have r ' (t)=-2 sin(2t) i +2 cos(2t) j + k and r ' '…

Q: Consider the vector function given below. r(t) = (t, 4 cos(t), 4 sin(t)) %3D (a) Find the unit…

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A: For the solution follow the next step.

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Q: 14. Given F(1) = (-1,3,0) F'(1) = (2,–2, 1) F"(1) = (0,–1, 4), What %3D is the vector equation of…

A: We will use basic vector calculus here to solve this question.

Q: Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this…

A: Given position vector is rt=cos2ti+sin2tj+tk

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