Show that F of F. = (2xy + z³)i+x²+3xz²k is conservative force field. Find the scalar potential

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

A:

Q: Prove that gradient of vector potential is zero

A: See the attachment

Q: Find work done by the force field f = (XY, 2, 42) when a Particle moves along the straight line from…

A: The force field is given as,find work done by the force field F when a particle moves along the…

Q: Find the mass of a wire that lies along the curve r(t)= (t² – 8) j+2tk, 0≤t≤2, if the 3 density is…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: X p(x, y, z)=xz²+sin (y) ex

A:

Q: 2. Find the gradient of the following scalar functions: a) T = 8/(x+y+2:²) b) V=3x²y³z c) U =…

A:

Q: Show that F : R^2 → R^2,F(x,y) = (x + y^2,2xy + 2y^2) is a gradient vector field, and find the…

A:

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

A:

Q: Show that the vector field F = (x² cos y, e+y) is not a gradient vector field. %3D

A:

Q: The magnetic field along a solenoid is conservative and given by 2xy 7- (2 x ₁-2x, (x²+1)-2). ¡−2x,…

A: Given a vector field as F=2xyx2+1-2x,lnx2+1-2 We need to find the scalar potential from which this…

Q: What is the work done by a force field F (x, y) := 2x to move a particle in a straight line from (0,…

A:

Q: Find the work done by F over the curve in the direction of increasing t. F = 4zi + 4xj + 4yk, r(t) =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: A Particle moves 2 X half way around the circle y² = 4 oriented in the counter-clockwise direction…

A: Given force field: and the path of the particle moving half way around the circle  in the…

Q: Line segment D runs from (1, -4, 3) to (2, 0, -1). Determine how much work is done by the force…

A:

Q: F - () (3x²y²z and F = 2r³yz Q.)11.1 Be (a) Explain why vector fields are conservative. (b)…

A:

Q: Let F(x, y) = (e, e-). Determine the integral curves for the vector field.

A: Given vector field F(x,y)=ex, e-xWe need to find the integral curve.

Q: Calculate the work expended when a particle is moved from 0 = (0,0) to Q = (1, 1) along the segments…

A:

Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…

A:

Q: Consider the vector field F(2. v) = (--2) i + (8ry° tan ' y) j. i + (8ry² – tan ' y) j. a) Is F…

A: Consider the vector field

Q: find the work done by the force field F(x,y) =(2y+x²,x²-2x) acting on an object as it moves along…

A: Given: The force field, Fx,y=2y+x2,x2-2x.   To find: The work done by the given force field acting…

Q: Sex. (x+y)ds where C is the straight-line segment x = 3t, y = (3-3t), z = 0 from C (0,3,0) to…

A:

Q: Find the potential function f for the field F = 6x i + 6y j + 7z k. A general expression for the…

A: Note: As you have posted multiple question but I will answer first question according to the…

Q: 1. Write down the general form of an order three linear ordinary differential equation. 2. Find all…

A: We have to write the general form of an order 3 linear ordinary differential equations.

Q: 2. Suppose p, q: (a, b| Note: You do not need to provide reasons in part (b). You'll discuss the…

A:

Q: To explore how different the computation can be if we have different integration orders, consider…

A: Given ,               ∫∫R xe-xy dA over the rectangle  R : 0≤x≤2 , -1≤y≤3  .

Q: Prove that F = (y' cosx+z')î +(2ysin x-4)ĵ+(3xz² +2)k is a conservative force field, find its scalar…

A: