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? then ? ? ? Are the following statements true or false? 1. If 7 is a vector field in 3-dimensional space, and W is a solid region with boundary surface S, dà = | W JF. S ? [[] div(F) dV. 2. If F is a vector field in 3-dimensional space, then grad(div(F)) = ở. 3. If F· dà = 12 and S is a flat disk of area 4, then div(F) = 3/. S 4. If I is a vector field in 3-dimensional space satisfying div(F) 1, and S is a closed surface ]] F. dA is equal to the volume enclosed by S. S oriented outward, then 5. If F and G are vector fields satisfying div(F) = div(G), then F = G.

? then ? ? ? Are the following statements true or false? 1. If 7 is a vector field in 3-dimensional space, and W is a solid region with boundary surface S, dà = | W JF. S ? [[] div(F) dV. 2. If F is a vector field in 3-dimensional space, then grad(div(F)) = ở. 3. If F· dà = 12 and S is a flat disk of area 4, then div(F) = 3/. S 4. If I is a vector field in 3-dimensional space satisfying div(F) 1, and S is a closed surface ]] F. dA is equal to the volume enclosed by S. S oriented outward, then 5. If F and G are vector fields satisfying div(F) = div(G), then F = G.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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? ? ? them [[it. S 1 ? Are the following statements true or false? ? 1. If F is a vector field in 3-dimensional space, and W is a solid region with boundary surface S, || F · dà = I div(F) dv. W 2. If 7 is a vector field in 3-dimensional space, then grad(div(F)) = 0. "! F.dA = 12 and S is a flat disk of area 4, then div(F) = 3/ñ. S 4. If I is a vector field in 3-dimensional space satisfying div(F) = 1, and S is a closed surface oriented outward, then F. dà is equal to the volume enclosed by S. 3. If S 5. If I and G are vector fields satisfying div(F) = div(G), then F = G.
Transcribed Image Text:? ? ? them [[it. S 1 ? Are the following statements true or false? ? 1. If F is a vector field in 3-dimensional space, and W is a solid region with boundary surface S, || F · dà = I div(F) dv. W 2. If 7 is a vector field in 3-dimensional space, then grad(div(F)) = 0. "! F.dA = 12 and S is a flat disk of area 4, then div(F) = 3/ñ. S 4. If I is a vector field in 3-dimensional space satisfying div(F) = 1, and S is a closed surface oriented outward, then F. dà is equal to the volume enclosed by S. 3. If S 5. If I and G are vector fields satisfying div(F) = div(G), then F = G.
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