Question: Consider the vector field F ( x , y , z ) = ( 3 z + 3 y ) i + ( 5 z

Consider the vector field F(x,y,z)=(3z+3y)i+(5z+3x)j+(5y+3x)k.
a) Find a function f such that F=f and f(0,0,0)=0.
f(x,y,z)=
b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral C Fdr.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

For each of the following decide whether the vector field could be a gradient vector field. Be sure that you can justify your answer. (a) F(x, y, z) = 3yi + 3x } F(x, y, z) is ? (b) F(x, y, z) = 2xi+...

Q:

Consider a vector field F (x, y, z) = x i - z k . a) Show that the source (i.e., divergence) F and vortex (i.e., rotor) F of the vector field F are both zeros. b) Based on the previous point, the...

Q:

9(a) (1 point) Consider the vector field F (x, y, z) (2z + 5y) i+ (4z + 5x)j+ (4y + 2x) k. a) Find a function f such that F = Vf and f(o, 0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0,...

Q:

12 (1 point) Consider the vector field F (x, y, z) = (2z + 4y) i + (2z + 4x) j + (2y + 2x) k. a) Find a function f such that F - Vf and f(0, 0, 0) = 0. f (z, y, z) = b) Suppose C is any curve from...

Q:

We consider the vector field F~ (x, y, z) = (x y)~i + (y +x)~j + ~k. Let S be the oriented cylindrical band x^2 + y^2= 9, 0 z 2, with the normal vector ~n pointing towards the outside as in the...

Q:

Solve the following question and DO NOT use the formulas given in the second image Consider the vector field F (x, y, z) = = (z, y, zx) And also consider the surface S of the tetrahedron enclosed by...

Q:

Consider the vector field F (x, y, z) = (x, 2, 2x) And also consider the surface S of the tetrahedron enclosed by the coordinate planes and the plane 19/8 + + = 1 . You may assume this surface has...

Q:

Consider the vector field F (x, y, z) = (x, 2, 2x) And also consider the surface S of the tetrahedron enclosed by the coordinate planes and the plane 19/8 + + = 1 . You may assume this surface has...

Q:

Consider the vector field F (x, y, z = Consider the vector field F T, y, z ax sin y 2z2 , by2z 2x4 cos For what values of a, b, c is the vector field F x, y, z 2y3 -h conservative in IR3 ?

Q:

11. [-/0.25 Points] DETAILS LARCALC11 15.1.039. Determine whether the vector field is conservative. F (x, y ) = xe* * 4/ (2yi + xj) O conservative O not conservative If it is, find a potential...

Q:

In this discussion, your should describe the importance of conducting regular wireless audits and the actions that should be taken as part of a wireless audit.

Q:

Explain the working of electrostatic Voltmeters with dia

Q:

C Company sells products to B Company on an account with payment terms of 2/10, net 30. On the purchase date, B Company will record a credit to accounts payable credit to cash credit to inventory...

Q:

Marigold Corp. purchased from its stockholders 5,300 shares of its own previously issued stock for $270,300. It later resold 1,700 shares for $54 per share, then 1,700 more shares for $49 per share,...