d the work done by the force field F in moving a particle along the curve C. F = xyi + 3j + 9xk; C:x = cos 6t, y = sin 6t, z = t, 0 sts- 12

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

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Q: C: r2 = cos20 bow right loop along the curve c defined above, using Green's theorem. F = (x +…

A: We have to find the work done by green theorem.

Q: Find the work done by the force field F in moving a particle along the curve C. F(x, y) = (x - y°)i+…

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Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

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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: 4. Find the work done by the force field F = (x? sin(y),y) on a particle that moves along the cubic…

A: Given: The force field, F→=x2siny,y on a particle that moves along the cubic y=x3 from 1,1 to 2,8.

Q: 12 Integrate: ,V4 - z² + dr

A: The given function is 4-x2+x7+24-x2 We have to integrate this function over the interval -2, 2

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: Sketch a directional field for the equation. Identify at least 3 isoclines. dy dx =y-x+2

A: This is a problem of slope field.

Q: A force F acts on a particle that is moving in the plane along the semi-circle parameterized by 7(t)…

A: Given that: γt=−costi+sintj; t∈0,π F=x2+y2τ, τ is the unit vector tangential to the path. To…

Q: Question 3. Find the work done by the force fie ld F = xyi+y 2j in moving a particle along the curve…

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Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = sin 8y i + cos 2x…

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Q: Find the work done by the force field F(x, y) = x sin(y) i + yj on a particle that moves along the…

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Q: 6. A particle moves so that its position vector is given by i =sin 5tî – cos 5tj , where t is the…

A: Consider the given position vector. r→=sin5ti⌢−cos5tj⌢ Now, calculate the velocity vector of the…

Q: Consider r(t)=⟨sin(t),cos(t),2t⟩ the position vector of a particle at time t∈[0,3], where the…

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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: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+1

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Q: A particle moves along the graph of y = cos r so that the r-component of acceleration is always 2.…

A: Use the given information carefully.