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If f is a scalar field and F, G are vector fields, then fF, F· G, and F × G are defined by the following. (FF)(x, у, 2) 3D f(x, у, z) F(x, у, 2) (F : G)(x, у, 2) %3D F(x, у, 2) . G(х, у, z) (Fx G)(х, у, z) %3D F(x, у, 2) х G(x, у, z2) Find an identical expression, assuming that the appropriate partial derivatives exist and are continuous. curl (F + G) div F + div G G· curl F - F• curl G O curl F + div G curl F + curl G none of the above

If f is a scalar field and F, G are vector fields, then fF, F· G, and F × G are defined by the following. (FF)(x, у, 2) 3D f(x, у, z) F(x, у, 2) (F : G)(x, у, 2) %3D F(x, у, 2) . G(х, у, z) (Fx G)(х, у, z) %3D F(x, у, 2) х G(x, у, z2) Find an identical expression, assuming that the appropriate partial derivatives exist and are continuous. curl (F + G) div F + div G G· curl F - F• curl G O curl F + div G curl F + curl G none of the above

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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If f is a scalar field and F, G are vector fields, then fF, F· G, and F x G are defined by the following. (FF)(x, у, 2) 3 f(x, у, z) F(x, у, z) (F: G)(x, у, 2) %3D F(x, у, 2) G(х, у, z) (Fx G)(х, у, z) %3D F(x, у, z) x G(x, у, z) Find an identical expression, assuming that the appropriate partial derivatives exist and are continuous. curl (F + G) div F + div G G• curl F -F• curl G curl F + div G curl F + curl G none of the above
Transcribed Image Text:If f is a scalar field and F, G are vector fields, then fF, F· G, and F x G are defined by the following. (FF)(x, у, 2) 3 f(x, у, z) F(x, у, z) (F: G)(x, у, 2) %3D F(x, у, 2) G(х, у, z) (Fx G)(х, у, z) %3D F(x, у, z) x G(x, у, z) Find an identical expression, assuming that the appropriate partial derivatives exist and are continuous. curl (F + G) div F + div G G• curl F -F• curl G curl F + div G curl F + curl G none of the above
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