8 4 Ĝ(Xx, y, z) = 2x +y 2xz, 2х + у Зу? сos(Зпz),3пуз sin(Злz) — х2 1. Determine the potential function of G that will give (2,2,1) = 2 2. Determine the work done by G along the curve with parametrization R(t) = (2 – t, – cos(nt),3*),t E [0,1]

Q: Consider the function g defined by 1 g(x, y) = sin (TVry) + log3(x – 3y) Do as indicated. 1.…

A:

Q: In words, describe the curve r(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to a -- give enough…

A: To Explain: The parametric curve is r(t)=(2sint,et,2cost) for 0≤t≤6π , so that its graph can be…

Q: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 4

Q: Without finding T and N, write the acceleration of the motion a(t) to the position vector r(t) =…

A:

Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

A:

Q: c) Given the scalar function p(x, y, z) = x²e - y³ + cos 2z. Find the directional derivative of p(x,…

A:

Q: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

A:

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A:

Q: Show that the force F = (y^²2² - 6xz² ) ₁² + ²xyz²³ j^² + (3 xy² z ²-6x²²Z) k IS Conservative, hence…

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: The given potential function is Vx,y,z=2x2-5xy+xyz. (a) To Find: Rate of change of the function at…

Q: The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to $(r) : equi-…

A: The formula to calculate the vector which is normal to the equipotential  line of the potential…

Q: WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗…

A: Given :- The curve C parametrized by the vector equation r t = 3 sin t i^ +2 - sin t +cos t  j^…

Q: 6. Let f(x, y) = ln(2x - y²). (a) (b) (c) Determine the gradient of f at the point (2, -1).…

A:

Q: Solve this equation: ди + a = at %3D u(0,t) = 0 %3D ди (L, t) = 0 az u(z,0) = 2 %3D

A:

Q: Find the outward flux of F = (4x +25y*,0,) 10z through the surface 25 4 9

A: Solution:-

Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

A:

Q: At time t=0 a particle at the origin of an x⁢y⁢z-coordinate system has a velocity vector of…

A: Using the basic general velocity formula, we get the velocity vector of the particle at time t to be…

Q: 10. A particle moves in the xy-plane so that the position of the particle is given by x(1) =1+cos t…

A:

Q: directional deriva

A:

Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: nd the increase rate of the scalar V at point P from origin to the point P(12 , 1,11 here V=…

A: As gradient of a scalar function gives the magnitude and direction of rate of change.

Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

A:

Q: Let F = (t + 4) i +² sin(41) j+ t^k, G = e' i+ 4f* cos(t) j+ e$t* k and 512 -i+ 4² j+te²ª k 1 +t H =…

A: Given :  F=(t+4)i+t^ 2 sin(4t)j+t^ 4 k G=e^ t i+4t^ 4 cos(t)j+e^ 5t^ 2  H = (t ^ 5)/(1 + t) * i + 4t…

Q: Compute the work done by the force F = (sin(x + y), xy, x²z) in moving an object along the…

A: Given information:Force vector in Newtons.Initial point .Intermediate point .Final point .To find:…