are the units in the cylindrical and spherical coordinate system constant vectors?

Question

Arun · Answer

Any vector field can be written in terms of the unit vectors as: The spherical unit vectors are related to the cartesian unit vectors by: Note: the matrix is an orthogonal matrix, that is, its inverse is simply its transpose.

Khimraj · Answer

No. Consider, just for example, the unit vectors in cylindrical coordinates: 𝜌̂ 𝜌̂ 𝐳̂ =cos𝜙𝐱̂ +sin𝜙𝐲̂ =−sin𝜙𝐱̂ +cos𝜙𝐲̂ =𝐳̂ . By inspection, you can see that they cannot be constant, because they depend on the variable 𝜙.

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are the units in the cylindrical and spherical coordinate system constant vectors?

are the units in the cylindrical and spherical coordinate system constant vectors?

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are the units in the cylindrical and spherical coordinate system constant vectors?

are the units in the cylindrical and spherical coordinate system constant vectors?

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