The work W done by a constant force F in moving an object from a point A in space to a point B in space is defined as W = F· AB .

Q: Think About It Considera particle that is moving along the space curve given by r,(t) = t³i + (3 –…

A: The particle is  moving along the space curve: r1(t)=t3i +(3-t)j+2t2k Now, the partical r2(t) that…

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Q: A) find the directional derivative of f at P x - y f(x, y) = ; P(-1, –2); 0 = 1/2 x +y B) Find the…

A: Sorry, we can answer the first question as per the honor policy. Please resubmit the other question…

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x, y, z)…

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Q: 38. Motion along a circle Show that the vector-valued function r(t) = (2i + 2j + k) %3D + cos t V2…

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A: Draw the cube formed by the planes and Plot the coordinate of point Q. Observe the figure carefully.

Q: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z)…

A: The position vector,

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Adding the plane surface y=0 to close the surface and apply the gauss divergence theorem.

Q: Use Green's Theorem to find the work done by the force F(x, y) = x(x + y) i + xy² j in moving a…

A: Given that, F=x(x+y)i+xy2j So Work done is ∫CF.dr=∫Cx(x+y)i+xy2j.dr Green's Theorem:…

Q: How much is the work now worth if we take F(x, y) = (αx, αy), where α is any positive constant?

A: Work North worthhh

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x, y, z)…

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Q: The force exerted by an electric charge at the origin on a charged particle at the point (x, y, z)…

A: In this question we have to find work done when we have given force this the above mathematical…

Q: Zero component of the curl For what vectors n is(curl F) ⋅ n = 0 when F = ⟨y, -2z, -x⟩?

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Q: The concentration of salt in a fluid at (x, y, z) is given by F(x, y, z) = 3x2 + 2y4 + 4x2z? mg/cm3.…

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Q: ntegral calculus A particle moves according to the given acceleration function over the given…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

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Q: Vector A =x-a, + 2y · a, – z · az, please: 1. Express A in cylindrical and spherical coordinate 2.…

A: Given: A=x·ax+2y·ay-z·az To express: A in cylindrical and spherical coordinate. To evaluate: A at…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

Q: Find the work done by a force F = 8i – 6j + 8k that moves an object from the point (0, 5, 7) to the…

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Q: y Consider the surface of equation z = What is the equation for the tangent line to S at x2+y4 * the…

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Q: se Green's theorem to find the work done by the force F(x, y) = x(x + y) i + xy²j in moving a…

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Q: Work integral Find the work done in moving an objectfrom P(1, 0, 0) to Q(0, 1, 0) in the presence of…

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Q: V = [3x-y, x² -ky²] In the force field defined by the vector, a particle moves from point A(-2,-1)…

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Q: Cylindrical coordinates (p, ó, z): ê, = cos o î + sin ø 3, ês = - sin ø î + cos o ĵ, êz = k (4) (5)…

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Q: F = in the displacement The work done by the force along the path C:y=x from the point (0,0) to…

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Q: The force exerted by an electric charge at the origin on a charged particle at the point (2, y, z)…

A: To find the work done as the particle moves along the straight line from (2, 0, 0) to (2, 3, 5).

Q: A constant force F = 3i +5j +10k moves an object along the line segment from (1, 0, 2) to (5, 3, 8).…

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Q: The force exerted by an electric charge at the origin on a charged particle at the point (x, y, z)…

A: Given :  The force vector f→r→=Kr→r→3 where K is constant. To find : The work done as the particle…

Q: The force exerted by an electric charge at the origin on a charged particle at the point (z, y, z)…

A: given force is                                                              F→(r→)=Kr→r→3 we have to…

Q: Find the work done by a force F = 8i – 6j + 8k that moves an object from the point (0, 5, 7) to the…

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Q: Calculate the work done by the force field on the particle.

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Q: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z)…

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Q: 12) The work W done by a constant force F as its point of application moves along the vector PQ is…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: A) find the directional derivative of f at P x- y. f(x, y) = ; Р(-1,-2); 0%- п/2 x+y B) Find the…

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Q: 35-38 - Calculating Work Find the work done by the force F in moving an object from P to Q. 35. F =…

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

Q: Two electrons r meters apart repeleach other with a force ofF = 23 * 10-29/ r2 newtons. Suppose one…

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Q: Use Green's theorem to find the work done by the force F(x, y) = x(x + y) i + xy2j in moving a…

A: Given force is: F(x,y)=x(x+y)i+xy2jWe have to find the work done by the given force using Green's…