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31. If F = Mi + Nj + Pk is a differentiable vector field, we define the notation F· V to mean + N- дх ду dz For differentiable vector fields F and F2, verify the following identities. а. х (F X F) 3 (F, V)F — (F - DF, + (V -F)F, - (V•F;)F, b. V(F, · F,) = (F¡ · V)F, + (F, · V)F, + F¡ × (V × F,) + F, x (V X F,)

31. If F = Mi + Nj + Pk is a differentiable vector field, we define the notation F· V to mean + N- дх ду dz For differentiable vector fields F and F2, verify the following identities. а. х (F X F) 3 (F, V)F — (F - DF, + (V -F)F, - (V•F;)F, b. V(F, · F,) = (F¡ · V)F, + (F, · V)F, + F¡ × (V × F,) + F, x (V X F,)

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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31. If F = Mi + Nj + Pk is a differentiable vector field, we define the notation F· V to mean + N- дх ду dz For differentiable vector fields F and F2, verify the following identities. а. х (F X F) 3 (F, V)F — (F - DF, + (V -F)F, - (V•F;)F, b. V(F, · F,) = (F¡ · V)F, + (F, · V)F, + F¡ × (V × F,) + F, x (V X F,)
Transcribed Image Text:31. If F = Mi + Nj + Pk is a differentiable vector field, we define the notation F· V to mean + N- дх ду dz For differentiable vector fields F and F2, verify the following identities. а. х (F X F) 3 (F, V)F — (F - DF, + (V -F)F, - (V•F;)F, b. V(F, · F,) = (F¡ · V)F, + (F, · V)F, + F¡ × (V × F,) + F, x (V X F,)
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