It is to be shown that the unit vectors in a cylindrical coordinate system are related to unit vectors in cartesian coordinate system by given relations. Concept Introduction: The parameters used to define a cartesian coordinate system are x , y , and z , where x defines the distance on x -axis, y defines the distance on y -axis, and z defines the distance on z -axis. The parameters used to define a cylindrical coordinate system are r , θ , and z , where r defines the radial distance from the point of reference, θ defines the direction of the point from the reference point, and z defines the perpendicular distance. The relationship between x , y , z and r , θ , z are: x = r cos θ y = r sin θ z = z

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Chapter 1, Problem 1.7P

Interpretation Introduction

Interpretation:

It is to be shown that the unit vectors in a cylindrical coordinate system are related to unit vectors in cartesian coordinate system by given relations.

Concept Introduction:

The parameters used to define a cartesian coordinate system are x,y, and z , where x defines the distance on x -axis, y defines the distance on y -axis, and z defines the distance on z -axis.

The parameters used to define a cylindrical coordinate system are r,θ, and z , where r defines the radial distance from the point of reference, θ defines the direction of the point from the reference point, and z defines the perpendicular distance.

The relationship between x,y,z and r,θ,z are:

x=rcosθy=rsinθz=z

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