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- Thread starter sams
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In summary, the conversation discusses the definitions of the unit vector ##\hat{φ}## in cylindrical coordinates and whether it can be obtained by evaluating the cross-product of ##\hat{ρ}## and ##\hat{z}## or by using the right-hand rule. The direction of ##\hat{φ}## is typically defined as anti-clockwise when looking down the z-axis.

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Thank you so much for your help...

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sams said:

Thank you so much for your help...

It's all here:

http://mathworld.wolfram.com/CylindricalCoordinates.html

##\phi## (or ##\theta## to mathematicians) is usually defined to be anti-clockwise looking down the z-axis.

- #3

Unit vectors in cylindrical coordinates are a set of three mutually perpendicular vectors, known as *r*, *θ*, and *z*, that are used to describe the position and orientation of a point in three-dimensional space. They have a magnitude of 1 and are used to define the direction of each coordinate axis.

In cylindrical coordinates, the unit vectors are typically represented as *ĉ _{r}*,

The unit vectors in cylindrical coordinates can be calculated using the following equations: *ĉ _{r} = cos(θ) i + sin(θ) j *

ĉ_{θ} = -sin(θ) i + cos(θ) j

ĉ_{z} = k

*The unit vectors in cylindrical coordinates, ĉ_{r}, ĉ_{θ}, and ĉ_{z}, can be expressed in terms of the standard Cartesian unit vectors, i, j, and k, using the following transformation equations: *

ĉ_{r} = cos(θ) i + sin(θ) j

ĉ_{θ} = -sin(θ) i + cos(θ) j

ĉ_{z} = k

*Unit vectors in cylindrical coordinates are commonly used in physics and engineering to describe the position, orientation, and motion of objects in three-dimensional space. They are particularly useful in situations involving cylindrical symmetry, such as in fluid dynamics, electromagnetism, and structural mechanics. They are also used in transformations between different coordinate systems and in vector calculus applications.*

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