7. Consider the Helix: r(t) = (R cost, R sint, Rt), 0 ≤ t ≤ 2π for R a constant. A. Calculate the work in the presence of F = (-y, x,-z) when moving a particle along r(t) from t = 0 to t = 2π. B. Calculate the mass of a wire in the shape of the helix r(t) from t = 0 to t = π with density 8(x, y, z) = x + y.

Q: #2. Consider the following vector function. r(t) = (t,3t²,-t²). (a) Find the arc length function.…

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Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: A particle moving along the curve (t) = (cost+t sint)i + (sint - cost)j,find acceleration components…

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Q: Q3. For the motion vector r(t) = e cost i + e'sint j %3D find: (i) (ii) ат

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Q: Evaluate F dr where F(x, y, z)=(x, xy, yz) and C is the curve r (t) = (t, t

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Q: Find curvature of the parametric curve r(t) = (t, t3 – t, 3) at t = 1. Show your work.

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Q: Q3. The acceleration of a particle moving in space is a(t) = (-3cost)i + (-3sint)j at t = 0 the…

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Q: 3. Consider the curve defined by the parametrization r(t) = (t cost, tsint, 232t³/2), t € [0,67],…

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Q: what's the final answer to a and b?

A: The objective of the question is to find the moment of time t0 and the point P0 on the curve r(t)…

Q: Q2. A particle moving along the curve R(t)=(cost +1 sint)i + (sint -t cost)j,find acceleration…

A: Solution:

Q: Consider the space curve r(t) = (cost cos 2t, cost sin 2t, sin t). (a) Find r(t).

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Q: Evaluate f, x*dz + z*dy + y*dx where C is the curve x = t,y = t, z = t? from t= 0 to t= 2.

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Q: Find the torsion of the helix r(t) =(cost, sint,t).

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