(x, y, z is F(r) = Kr/|rl3where K is a constant. Find the work done as the particle moves along a straight line from The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = (5, 0, 0) to (5, 2, 3)

Q: Suppose that over a certain region of space the electrical potential V is given by V (x,y,z) = 3.x²…

A:

Q: Determine the flow rate of water across the net if the velocity vector field for the river is given…

A: The given velocity vector field is,V=<x-y, z+y+4, z2>The net is given as:x2+z2≤1 and y=0Assume…

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

A: The force exerted by an electric charge at the origin, at the point (x, y ,z) is, F=krr3 where,…

Q: 1. The air pressure in a particular room varies from point to point and is given by p(x. y. 2) = 3x°…

A: Hello. Since your question has multiple parts, we will solve the first question for you. If you want…

Q: Find the directional derivative of f(x,y,z)=z^3−x^2y at the point (-1, 1, -4) in the direction of…

A:

Q: Find the directional derivative of f(r, y, z) = yr + z* at the point (2, 3, 1) in the direction of a…

A: Directional Derivative of a Function of Three Variables =>Directional derivative of  f ( x , y ,…

Q: Find the directional derivative of f(x, y, z) = zy + xª at the point (2, 1, 3) in the direction of a…

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

Q: Find the work that is done by the force F = (x + y)î + xyj – z?k acting on a particle that moves…

A: Convert function into parametric function. Then find work done by doing line integration.

Q: Find a unit vector n that is normal to the surface 4z? – 2x* – 3y = 14 at P = (1,2, 4) that points…

A: To Determine: Find the unit normal n that is normal to the surface at p(1,2,4) that points in the…

Q: Suppose given a function f(x, y, 2) of three variables, and a point (o, y0, 20) €R. Explain in your…

A:

Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

A:

Q: Determine the work done by the force F"(x,y,z)=(x²y,xy). to move a particle along the line segment…

A:

Q: Determine the rate of change at (0, 2) of the function 1 h (x, y) V1+x² + 2y² in the direction of…

A:

Q: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at…

A:

Q: Find the directional derivative of f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

Q: Find the directional derivative of the function f(x,y, z) = V22+ y² + z² at point (2, -3, 6) in the…

A: In this question, we want to find the directional derivative of the given function at given point…

Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

A:

Q: Compute the vector line integral: x – 4 dx + (x – 4)² + y² -y dy :- 4)2 + y² where C is the circle…

A: To find the below vector integral. ∮C−yx−42+y2dx+x−4x−42+y2dy

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

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

A: Given: fx,y,z=3x+7yz 1,7,-1 To find: Maximum rate of change of f at the given point. The…

Q: Find a unit vector in the direction in which f (x, y, z) = 3x³z² + 3y°z + 24z – 4 increases most…

A:

Q: Let f(x, y, 2) = cos(ryz) Find the directional derivative of f at the point (,, 7) in the (a)…

A: We have to find Directional Derivative and Largest possible value.

Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: 3. Find the directional derivative of f(x, y, z) =x*y-yz' +z at the point (1, -2,0) in the direction…

A:

Q: Find the Vector function that represents the curve of the intersection of the two surfaces.  The…

A: Given equations are x2+y2+4z2=4 ..... (1) and x2+z2=1 ..... (2) From equation (1) z2=(4-x2-y2)/4…

Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: 2 xy". - I + 3x'y". 2 →(2(3-t)(45+24)' ((33-t)"( 43+2€)² 6. Find the unit vector for which the…

A:

Q: Find the directional derivative of f(x,y,z)=xe +ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

Q: The pressure at the point (x, y, z) of a gas is given by P = f(x, y, z) = (x, y) = 40 + 5x2 + 2y2 +…

A:

Q: Find the directional derivative of the function f(x, y, z) = /ryz at the point P(2,2, 2) in the…

A: Topic-vector calculas

Q: The electrical potential (voltage) in a certain region of space is given by the function V(x, y, z)…

A:

Q: Find a unit vector n that is normal to the surface 4z? – 2x* – y = 18 at P = (1,2,3) that points in…

A: Solution of question is written in below steps.

Q: Find the directional derivative of f(x,y, z) = yz +x? at the point (3, 2,1) in the direction of a…

A:

Q: What is the rate of change of the function f(x,y) = ye^(2cos x) + tan(x+3y) at ( 3π/2 , π/2) in the…

A: Given: fx,y=ye2cosx+tanx+3y To Find: Rate of change of fx,y in the direction of the vector 3,4 at…

Q: The directional derivative of f(x, y) = xe + cosxy at P,(2,0) in the direction of the vector 3i - 4j…

A:

Q: Compute for the directional derivative of f (x, y, z) = tan (Tx – 21ny)e4y-z at the point (, 0, In…

A:

Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…

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

A: Given that  r=x,y,z is Position vector Force exerted by an electic charge at the origin F=Krr3…

Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: If f (x, y, z) = xy + xz + yz, find this function's directional derivative at (-1,3,5) in the…

A:

Q: For the function f(x,y, z) := 10r + 7y³ + 723 + 9ry + 6yz+ 12rz+ 19 find the gradient at the point…

A:

Q: Compute the directional derivative and gradient of f(x, y, z) = 4r – yez at (2, -1,0) in the…

A: Given: fx,y,z=4x-y2e3xz       at     2,-1,0 Directional Derivative = Gradient of function x unit…

Q: 2. Compute the vector line integral: -y х — 4 Le (x – 4)² + y² dx + (x – 4)2 + y² dy where C is the…

A:

Q: For f(x,y,z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: Since there are two questions posted, we will answer the first question posted (1). If you want the…

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

A:

Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to <2,1>

Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.

Q: Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,3,2) in the direction of a vector…

A:

Q: Find the work done by the force F(x, y, z) = (x, —z, 2y) in moving straight from (0,0,0) to (1,1,0),…

A: