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The Pythagorean theorem we use in rectangular coordinates also works in cylindrical and spherical coordinates; you just have to replace x,y,z with r,theta,phi or s,phi,z. When calculating the distance between two points, you can use the same distance formula in spherical and cylindrical coordinates, but you need a different formula for rectangular coordinates.

The Pythagorean theorem we use in rectangular coordinates also works in cylindrical and spherical coordinates; you just have to replace x,y,z with r,theta,phi or s,phi,z. When calculating the distance between two points, you can use the same distance formula in spherical and cylindrical coordinates, but you need a different formula for rectangular coordinates.

Advanced Engineering Mathematics
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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Which of the following is/are correct about calculating distances in rectangular and curvilinear (spherical and cylindrical) coordinate systems? (There may be more than one correct statement.) When calculating the distance between two points, you have to use a different distance formula for each coordinate system (rectangular, spherical, and cylindrical). ✓ The Pythagorean theorem we use in rectangular coordinates also works in cylindrical and spherical coordinates; you just have to replace x,y,z with r,theta,phi or s,phi,z. When calculating the distance between two points, you can use the same distance formula in spherical and cylindrical coordinates, but you need a different formula for rectangular coordinates. When calculating the distance between two points, you can use the same distance formula in rectangular, spherical, and cylindrical coordinates.
Transcribed Image Text:Which of the following is/are correct about calculating distances in rectangular and curvilinear (spherical and cylindrical) coordinate systems? (There may be more than one correct statement.) When calculating the distance between two points, you have to use a different distance formula for each coordinate system (rectangular, spherical, and cylindrical). ✓ The Pythagorean theorem we use in rectangular coordinates also works in cylindrical and spherical coordinates; you just have to replace x,y,z with r,theta,phi or s,phi,z. When calculating the distance between two points, you can use the same distance formula in spherical and cylindrical coordinates, but you need a different formula for rectangular coordinates. When calculating the distance between two points, you can use the same distance formula in rectangular, spherical, and cylindrical coordinates.
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