For the vector field: F = (x + y)i + (y + z)j + (z + x)k 1) Compute the flux out of the cube bounded by the planes {x = 1}, {y = 1}, {z = 1} in the positive octant {x ≥ 0, y ≥ 0, z ≥ 0}, use the divergence theorem 2) Now what if the cube is shifted and rotated to another portion in space, but still having the same dimension (i.e., it is still a 1 × 1 × 1 cube). Will your answer of part a change? 3) Is there a vector field G such that F=∇×G?

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A: This is a problem of vector calculus.

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A: We will use the basic knowledge of vector calculus and integral calculus to answer this question.

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Q: re f an -2, 3)

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