Paraboloidal coordinates u, v and ø are defined in terms of Cartesian coordinates by I = uv cos o, y = uv sin ø, Show that the u-component of V x à is given by (if ā is written in terms of the associated basis vectors, ā = a„ û + a, û + as $): 1 as das 1 да, (u² + v²)'/2 ( v dv uv dø
Paraboloidal coordinates u, v and ø are defined in terms of Cartesian coordinates by I = uv cos o, y = uv sin ø, Show that the u-component of V x à is given by (if ā is written in terms of the associated basis vectors, ā = a„ û + a, û + as $): 1 as das 1 да, (u² + v²)'/2 ( v dv uv dø
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Transcribed Image Text:|Paraboloidal coordinates u, v and o are defined in terms of
Cartesian coordinates by
x = uv cos o,
y = uv sin ø,
(u²-
Show that the -component of V x ã
is given by (if å is written in terms of the associated basis vectors,
d = au û + a, ô + as ¢):
das
dv
1
1 да,
(u² + v²)!/2
uv do
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