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F ⃗=(18z+6y+cos^2 (x^2 )) i ⃗+(sin^2 (y)+5z) j ⃗+(e^(z^2 )+12y)k ⃗

Let C be the circle of radius 7 in the plane x + y + z = 24, centered at (8, 8, 8) and oriented counterclockwise when viewed from the origin.

Find the exact value of c · d

https://brainmass.com/physics/flux-flux-density/exact-value-flux-integral-287182

## SOLUTION This solution is FREE courtesy of BrainMass!

Let C be the circle of radius 7 in the plane x + y + z = 24, centered at (8, 8, 8) and oriented counterclockwise when viewed from the origin.

Find the exact value of c · d

Using Stock's theorem,

Unit normal vector to the surface x + y + z = 24 is given by

Then

Where A is the area of the circle which is bounded by plane x + y + z = 24.

Thus =

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