Question 3. Find the work done by the force fie ld F = xyi+y 2j in moving a particle along the curve C, which is parametrized as r(t) = (sin t, 1+ t), 0

Q: 5t 2 A) Given the vector valued function: r(t) = 2 sin(t)i+ e' j-4cos(3t)k A) Find r(0) = B) Find…

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Q: The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find…

A: The position vector for particle moving on helix is ct=3cost, 2sint, t2. To find the speed of the…

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(at) î + at j+ sin(rt) k. %3D…

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Q: Find the work done by the force field F(r, y) = x²i+ xyj on a particle that moves once around the…

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Q: Let 7(t) = (t + 4, – e*, 3 sin(3t)) - Find the unit tangent vector T (t) at the point t = :0 T(0) =

A: We have to find

Q: F.dr. QUESTION 12 Let C be the oriented curve parameterized by r(t)=(t,t> for 0sts2 (so C is…

A: Vector calculus

Q: ind the work done by force F = zi + xj + yk in moving an object over the curve r(t) = sin ti+ costj+…

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Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

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Q: a) The position of point moving in space is given by R(t) = 3 tan t i + cott j +2 lnt k, find the…

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Q: consider a particle traveling within the force field F = along the parametrized curve r(t) = from…

A: Consider the given: F=−y,x,12rt=tcost,tsint,12tFrom point 0,0,0 to 2π,0,π. The work done moving the…

Q: Let 7(t) = (– 5t4 – 4, – 2e“, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0 T (0)…

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Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(zt) î + at j+ sin(rt) k. %3D…

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Q: At what times in the interval

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Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

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Q: for the attched r(t): 1) how do I find r'(t) 2) sketch the position vector r(0) 3) sketch the…

A: given that r(t)=e2ti+etj. we need to  : (a) find r'(t) r'(t) is the first derivative of the function…

Q: Find the work done by the force field F = in moving the particle from the point (3, 0, 0) to the…

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Q: 4. The particle moves along a plane curve y = e, where x and y are measured in meters. It has a…

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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: A force F acts on a particle that is moving in two dimensions along the semicircle x = 1 – cos 0, y…

A: Given the forces on a particle that is moving in 2D along the semicircle x=1-cosθ, y=sinθ, 0≤θ≤π.

Q: If an object travels in the xy-plane along the curve traced out by 
the vector function r(t) = (t…

A: We have to find the total distance traveled by the object from t = 0 to t = 4.

Q: 3- Calculate the curls of the following vector functions: (a) V = s(2 +sin Ø) s+ s sinØ cosØ Ø+ 3z…

A: V→=s2+sin2∅∅^+ s sin∅cos ∅ ∅ ^+3zz^ curl V→=∇×V→=s^∅^z^∂∂s∂∂∅∂∂zs(2+sin2s)s…

Q: Question 7. t = 1. ] Let r(t) = 5i + t²j – t²k. Compute the unit tangent vector T(t) at time

A: This is the problem of Vector Calculus.

Q: The position of point moving in space is given by R(t) = 3 tan t i+ cot t j + 2 lntk, find the…

A: We will find out the required velocity and acceleration vector functions.