Introduction to Electrodynamics · Problem 1.42

Vector Analysis — David J. Griffiths

Physics · curvilinear-coordinates-cylindrical

Problem

Express the cylindrical unit vectors s^\hat{\mathbf{s}}, ϕ^\hat{\boldsymbol{\phi}}, z^\hat{\mathbf{z}} in terms of x^\hat{\mathbf{x}}, y^\hat{\mathbf{y}}, z^\hat{\mathbf{z}} (that is, derive Eq. 1.75). "Invert" your formulas to get x^\hat{\mathbf{x}}, y^\hat{\mathbf{y}}, z^\hat{\mathbf{z}} in terms of s^\hat{\mathbf{s}}, ϕ^\hat{\boldsymbol{\phi}}, z^\hat{\mathbf{z}} (and ϕ\phi).

Related theory

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