Find the work done by the vector field F = ( – 2, – 4y, 2æ) in moving an object along C in the positive direction, where C'is given by r(t) = (sin(t), t, cos(t)), 0

Q: OSketch the vector field F(x, y) = -5i – 5j and calculate the line integral of F along the line…

A: Solution:-     Given that, F→ x,y=-5i∧-5j∧we have to calculate the line integral ∴we have to…

Q: Calculate the divergence of the vector field F (x, y, z) = − 10 sin(2xy)i — cos(x³y)j. (Give an…

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Q: Let 7 (t) = (t + 5, 5e“, 3 sin(5t)) Find the unit tangent vector T (t) at the point t = 0 T(0) = <

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Q: Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

A: If  is vector valued function which is differentiable and then the unit tangent of is given by

Q: Let r(t) = (-3t³-4, -3e¹, 5 sin( - 3t)) Find the unit tangent vector T' (t) at the point t = 0 T(0)…

A: r(t)=&lt;-3t3-4, -3e4t, -5Sin(-3t) &gt;

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: Let be a potential for the vector field F = (-24 x³z + 6 xyz², 3 x² z² + 15y¹, −6 x¹ + 6 x²yz - 10…

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Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Find the curl of the vector field F curl F= (5y cos(x), 2x sin(y)).

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Q: Let 7 (t) = (3t3 + 4, – 4ešt, – 5 sin(4t)) - Find the unit tangent vector T (t) at the point t = 0…

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Q: Let r(t)=sin(t + 1) + sin(t + 1)ĵ + √2 cos(t + 1) * denote the position of an object. (a) Find a…

A: Step 1:r(t)=sin(t+1)i+sin(t+1)j​+2​cos(t+1)k Step 2:tangent…

Q: We consider the vector field F = (xy², -x²y). Let C be the parabola y = = x² from the point (-1, 1)…

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