Soru 3 Test the vector field F to determine if it is conservative. ( 10x3y2 k z10 210 z11 Not conservative O Conservative Soru 4
Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = Vf. (If the vector field is not conservative, enter DNE.) F(x, y, z) = 4xyi + (2x2 + 10yz)j + 5y2k f(x, y, z) =
Determine whether or not is a conservative vector field. F(x, y) =Lye*+cosly))i + lett +xsin(y))}
4. Evaluate (F•dr for F(x, y, z)=(3xz)i +(2z - y)j+(22)k and с C:r(t)= (2t+1)i+(3).j+(5t)k, Ostsi
1. One of the two vector fields listed below is conservative. The other one is not conservative. (a) Determine which one of these fields is conservative. Label the conservative field F and and find a potential function f for it. Label the other field G and prove that G is NOT conservative. (b) Use the fundamental theorem of line integrals to compute SCF . dr, where C is the curve parameterized by (c) Compute Jc G-dr, where C is the...
Compute the curl of the following vector field. F = (32? sin y, 3xz? cos y, 6xz siny) The curl of Fis ( Oi+ ( Ok. +
(1 point) Determine whether the vector field is conservative and, if so, find the general potential function. F = (cos z, 2y!}, -x sin z) Q= +c Note: if the vector field is not conservative, write "DNE". (1 point) Show F(x, y) = (8xy + 4)i + (12x+y2 + 2e2y)j is conservative by finding a potential function f for F, and use f to compute SF F. dr, where is the curve given by r(t) = (2 sinº 1)i +...
Find the potential when F =-Vº, a conservative force of field defined by F = (3x’yz – 3yli + (xºz – 3x)j + (x*y+2z)k
(9 marks) QUESTION 4 a) Given vector field Éx,y,z) --yº coszi - 3xy cosz j+ xy" sinzk. Show that F is a conservative vector field. (4 marks) ii) Find the potential function, f such that F=Vf. (4 marks)
Only the Matlab part !!!
Question 2 For the following vector fields F determine whether or not they are conservative. For the conservative vector fields, construct a potential field f (i.e. a scalar field f with Vf - F) (a) F(z, y)(ryy,) (b) F(z, y)-(e-y, y-z) (c) F(r, y,z) (ry.y -2, 22-) (d) F(x, y, z)=(-, sin(zz),2, y-rsin(x:) Provide both your "by hand" calculations alongside the MATLAB output to show your tests for the whether they are conservative, and to...