Please help with the solution to the following problem. The book is very hard to follow. This is Vector Analysis (Vector Calculus). The second attachment is how the textbook defines scale factors. 2.Find the scale factors forU1U3Y = U1U3 + U2= ZU2x = U3, General Orthogonal Curvilinear CoordinatesScale factors:ƏR(i = 1, 2, 3)h;du;Vu|Displacement vector:dR = h1 du, ei + h2 duz ez + hz duz ezArc length:ds = (h; du + hị duž + hị duž)'/2Volume element:dV = h¡hzh3 du, duz duzGradient:1 ofe2h2 duz1 afe3hз диз1 afVf =hi dui

Given that x=u3, y=u1u3+u2, z=u1u3u2 Note: The position vector R=xi+yj+zk. Therefore,…

Answered: Find the scale factors for U1u3 x = U3,…

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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Please help with the solution to the following problem. The book is very hard to follow. This is Vector Analysis (Vector Calculus). The second attachment is how the textbook defines scale factors.

2.
Find the scale factors for
U1U3
Y = U1U3 + U2
= Z
U2
x = U3,

General Orthogonal Curvilinear Coordinates
Scale factors:
ƏR
(i = 1, 2, 3)
h;
du;
Vu|
Displacement vector:
dR = h1 du, ei + h2 duz ez + hz duz ez
Arc length:
ds = (h; du + hị duž + hị duž)'/2
Volume element:
dV = h¡hzh3 du, duz duz
Gradient:
1 of
e2
h2 duz
1 af
e3
hз диз
1 af
Vf =
hi dui

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