Mathematics, 05.05.2020 18:40 rosas8
Are the following statements true or false? 1. If F⃗ is a vector field in 3-dimensional space, and W is a solid region with boundary surface S, then ∬SF⃗ ⋅dS⃗ =∭Wdiv(F⃗ )dV. 2. If F⃗ and G⃗ are vector fields satisfying div(F⃗ )=div(G⃗ ), then F⃗ =G⃗ . 3. If ∬SF⃗ ⋅dS⃗ =12 and S is a flat disk of area 4π, then div(F⃗ )=3/π. 4. If F⃗ is a vector field in 3-dimensional space satisfying div(F⃗ )=1, and S is a closed surface oriented outward, then ∬SF⃗ ⋅dS⃗ is equal to the volume enclosed by S. 5. If F⃗ is a vector field in 3-dimensional space, then grad(div(F⃗ ))=0⃗ .
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