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Chapter 13: Q 71. (page 1068)

Let abe a constant. Prove that the equation of the plane x=aisrole="math" localid="1652390612497" 蚁=acsc蠒sec胃 in spherical coordinates.

Short Answer

Expert verified

Conversion is done usingx=蚁sin蠒cos胃,y=蚁sin蠒sin胃,z=蚁cos蠒.

Step by step solution

01

Given Information

Equation of plane in rectangular coordinates is given by x=a(ais constant).

02

Simplification

The spherical coordinates are given by following mathematical relation

x=蚁sin蠒cos胃,y=蚁sin蠒sin胃,z=蚁cos蠒

For the transformation of given plane to spherical coordinates, use x=蚁sin蠒cos胃in x=a.

蚁sin蠒cos胃=a

鈬�蚁=asin蠒cos胃

=a1sin蠒1cos胃

Hence,蚁=acsc蠒sec胃

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