If the relation between the spherical coordinates ' and the rectangular Cartesian coordinates x is given by x' = x' sin x? cos x? x2 = x' sin x? sin x3 = x' cos x? Then the metric tensor gij is equal to 0 (x!)2 (x'sinx?)²] 0 (x')? (zlcosz2)리 (x'sinx³)²] None of these 10

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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15
If the relation between the spherical coordinates and the rectangular Cartesian
coordinates x is given by
x' = x sin x? cos x2
x2 = x' sin x? sin x
x3 = x' cos x?
put of
Then the metric tensor gij is equal to
0 (x)2
(고sinx?)2
0 (x)2
(x'cosx?)2]
(x)2
(x'sinx³)²]
0.
O None of these
Transcribed Image Text:15 If the relation between the spherical coordinates and the rectangular Cartesian coordinates x is given by x' = x sin x? cos x2 x2 = x' sin x? sin x x3 = x' cos x? put of Then the metric tensor gij is equal to 0 (x)2 (고sinx?)2 0 (x)2 (x'cosx?)2] (x)2 (x'sinx³)²] 0. O None of these
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