Evaluate ∬V.ndσ if V=xcos2yi+xzj+zsin2yk over the surface of a sphere with centre at the origin and radius 3 a) 34π b) 37π c) 36π d) 40π Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Answer to Consider F and C below. F(x, y, z) = yze^xzi + e^xzj. Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Problem 2: Let F(x, y, z) = yzi + xzj + (xy + 2z)k . • Compute div(F). • Compute curl(F). Explain how you know that F is conservative. • Compute a potential for F. That is, find a function f(x, y, z) so that F=Vf. • Let C be any curve which starts at (0,0,0) and ends at (1,1,1). Com- pute F. dr S.

Verify stokes theorem for A = 3yi - xzj + yz^2 k where S is the surface of the paraboloid 2z = x^2 + y^2 bounded by z = 2 and C is its boundary. Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Prove that the Force field given by F = yi + xzj + zk is it conservative State three properties of conservative forces and give two examples Find a potential o that satisfies the relation F = -V0 2. Given Ø(x,y,z) Evaluate 10 wherer = + y2 + z2 3.

Question: Given F(x,y,z)=yzi+xzj+xyk, - (a) Show that F is conservative and find its potential function. - (b) Evaluate ∫CF⋅dr for the curve r1(t)=(6−2t)i+(1+t)j+(2+t)k, for 0≤t≤2.-

Consider the force field F(x, y, z) = yzi+xzj + xyk. (a) [3] Is F a conservative vector field? Justify your answer. (b) [2] Find the work done by the force field F above in moving a particle along the curve r(t) = cost i + cos² tj + cos (2t) k, Osts 1/2. [Hint: Is there a theorem you can use to help you with this problem?]

Cone F = y^2i + xzj - k outward (normal away from the z-axis) through the cone z = 2 squareroot x^2 + y^2, 0 lessthanorequalto z lessthanorequalto 2 Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Consider F and C below.F(x, y,z) = yz i + xzj + (xy + 6z)kC is the line segment from (1,0,-2) to (6,4,3)(a) Find a function f such that F = Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Answer to F(x,y,z)= 2yi+xzj+(x+y)k C is the curve of. Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.