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Vector Analysis — David J. Griffiths
Physics · curvilinear-coordinates-spherical
Problem Express the unit vectors r ^ \hat{\mathbf{r}} r ^ θ ^ \hat{\boldsymbol{\theta}} θ ^ ϕ ^ \hat{\boldsymbol{\phi}} ϕ ^ x ^ \hat{\mathbf{x}} x ^ y ^ \hat{\mathbf{y}} y ^ z ^ \hat{\mathbf{z}} z ^ r ^ ⋅ r ^ = ? 1 \hat{\mathbf{r}} \cdot \hat{\mathbf{r}} \stackrel{?}{=} 1 r ^ ⋅ r ^ = ? 1 θ ^ ⋅ ϕ ^ = ? 0 \hat{\boldsymbol{\theta}} \cdot \hat{\boldsymbol{\phi}} \stackrel{?}{=} 0 θ ^ ⋅ ϕ ^ = ? 0 r ^ × θ ^ = ? ϕ ^ \hat{\mathbf{r}} \times \hat{\boldsymbol{\theta}} \stackrel{?}{=} \hat{\boldsymbol{\phi}} r ^ × θ ^ = ? ϕ ^ x ^ \hat{\mathbf{x}} x ^ y ^ \hat{\mathbf{y}} y ^ z ^ \hat{\mathbf{z}} z ^ r ^ \hat{\mathbf{r}} r ^ θ ^ \hat{\boldsymbol{\theta}} θ ^ ϕ ^ \hat{\boldsymbol{\phi}} ϕ ^ θ \theta θ ϕ \phi ϕ Browse the problem library