Find the work done by the force F = 4xyỉ + (2x2 - 3xy)j by pushing a particle along the line segment from (-3, -2) to (1, 0) and the arc of the circle in the first quadrant from (1,0) to (0,1).

Q: Find the work done by the force F = 4xyi + (2x² – 3xy)j by pushing a particle along the line segment…

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Q: Find the work done by the force F = 9xy i + 6yj acting along the piecewise-smooth curve consisting…

A: Given that F=9xy i+6y2 j Let r=xi+yj+zk ⇒dr=dx i+dy j+dz k Now,  F.dr=(9xy i+6y2 j+0k)(dx i+dy j+dz…

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Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

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Q: A point moves along the intersection of the elliptic paraboloid z = 10x + 11y and the plane y = 1.…

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Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: Find the work done by a force F = 5i (mag-nitude 5 N) in moving an object along the line from the…

A: Given,

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Q: 0. for the funchion f (x,4) = 3-x?- u?, find a unit tangent vector to the level curve at the point…

A: Given: fx,y=3-x2-y2-3 at P3,5​​​​​​​

Q: Find the acute angle that a constant unit force vector makes with the positive x-axis if the work…

A: Given- a constant unit force vector makes with the positive x-axis if the work done by the force in…

Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: A point moves along the intersection of the elliptic paraboloid z = x + 3y² and the plane y = 3. At…

A: z=x2+3y2 and y=3 Point of Intersection : Curve z:x2+3y2=x2+3(3)2=x2+27 dzdx=2x+0 =2x

Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

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Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Find the equation on the plane tangent to the following surfaces at a given point: z=exy; (2,0,1)…

A: The equation on the plane tangent to the surface z = f(x, y) at a given point (a, b, c) is given by:…

Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

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Q: Evaluate F. dī where F = , and C' is the circle of - counterclockwise direction.

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Q: A body of mass 6 kg moves in a (counterclockwise) circular path of radius 6 meters, making one…

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Q: find the points on the surface + z² = 1 that have their tangent plane perpendicular to the vector…

A: For tangent plane of the surface f(x,y,z)=k at a given point normal vector to tangent plane  will be…

Q: Let the the position vecor be R(t) = (e' cos(3t) , e' sin(3t),0). Compute the unit tangent vector

A: The given position vector is R(t)=etcos(3t),etsin(3t),0 . compute the unit tangent vector T(t)=?

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A: As per our guidelines, we are allowed to answer only one question. Since you have posted multiple…

Q: Find the direction in which the maximum rate of change occurs for the functio f(r, y) = 2x sin(ry)…

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Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 7y and the planex = 1. At…

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Q: Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point…

A: The helix is given as x=sin 2t, y=t, z=cos 2t. We have to find the equation of the osculating plane…

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Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

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Q: The work done by the force F = in the displacement along the path C: r(t)=from the point (1,0,0) to…

A: To find the work done by a force

Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: A point moves along the intersection of the elliptic paraboloid z = 4x + 11y and the plane y = 4. At…

A: given information is z=4x2+11y2 The plane y=4To find :Rate of change of z with respect to x when the…

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Q: A curve is given by the parametrization r(t)= [²,-t, ť ]. If the tangent vector to this curve at a…

A: The given curve is,  ,

Q: The plane tangent to the surface z +1= re" cos z at (1,0,0) can be represented by the equation X + y…

A: Given: z+1=xey cosz

Q: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

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Q: Starting from the point (-4, 5, 4) reparametrize the curve r (t) = (-4- 3t)i + (5 – 3t)j + (4 + 2t)k…

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Q: Find the divergence and curl of the vector A = rz sin ø ↑ + 3rz² cos o and evaluate both answers at…

A: Consider the given vector. A=rzsinϕr^+3rz2cosϕϕ^ The divergence formula is defined as. divF=Px+Qy…

Q: 4. If a particle moves in the xy-plane so that at time t its position vector is sin 31 ,3r2 find the…

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Q: nit vector that is parallel to the

A: Here have to find the unit vector that is parallel to the line tangent to the parabola y = x2 at the…

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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