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...


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

Extracted 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,)

Jun 04, 2022
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