# Vector in cylindrical polar coordinates

1. Apr 20, 2004

### ilikephysics

The problem is:

Write the vector V=i+j+k=(1,1,1) at the point (x,y,z)=(1,1,1) in cylindrical polar coordinates. What is the gradient of the function phi=x(x^2+y^2)z at this point?

I don't know how to write the vector in cylindrical polar coordinates. I know that the coordinates are (r(perpendicular), theta, z). Can someone show me how to do this in cylindrical polar coordinates with an example?

Is the gradient of the funcition 4i+2j+2k at (1,1,1)?

2. Apr 20, 2004

### turin

The vector components in cylindrical polar coordinates depend on position. The position can be expressed in cylindrical polar coordinates as:

(ρ,θ,z)

where ρ is the perpendicular distance from the Cartesian z-axis, θ is the angle about the Cartesian z-axis that a line connecting the point to the Cartesian z-axis would make from the Cartesian x-axis, and z is the Cartesian z-coordinate. The Cartesian components of a vector transform into the cylindrical polar coordinates of a vector as:

vρ = (√(ux2+uy2))cos(θ-arctan(uy/ux))
vθ = -(√(ux2+uy2))sin(θ-arctan(uy/ux))
vz = uz

where

v = uxex+uyey+uzez = vρeρ+vθeθ+vzez

That's what I got.