(a) F(x, y,z)= 3x²y -2z'x+y'. (i) Find VF. (ii) Find the directional derivative F(x,y,z) at the point (1, 1, -1) in the %3B direction i-2j+k. (iii) Find V'F.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a)
F(x, y,z)=3x°y -2:'x+y'.
(i)
Find VF.
(ii)
Find the directional derivative of F(x, y,z) at the point (1, 1, -1) in the
direction i-2j+k.
(ii)
Find V'F.
(b)
A fluid with constant density has velocity u
=x'yi-xy'j.
(i)
Show that u satisfies the continuity equation.
(ii)
Calculate the vorticity of the flow.
Transcribed Image Text:(a) F(x, y,z)=3x°y -2:'x+y'. (i) Find VF. (ii) Find the directional derivative of F(x, y,z) at the point (1, 1, -1) in the direction i-2j+k. (ii) Find V'F. (b) A fluid with constant density has velocity u =x'yi-xy'j. (i) Show that u satisfies the continuity equation. (ii) Calculate the vorticity of the flow.
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