# Convert 3d cartesian to polar

• -EquinoX-
In summary, the problem at hand is to convert the given vector into polar coordinates. The suggested approach is to first express x, y, and z in terms of θ, φ, and r, and then rewrite the unit vectors in terms of e_θ, e_φ, and e_r. Finally, the substitution can be made to obtain the vector in polar coordinates. The forum may be experiencing issues with LaTeX.

## Homework Statement

I need to convert this to a polar coordinate
$$\vec{F} = 5xz\vec{i} + 5yz\vec{j} + 4z^3\vec{k}$$

## The Attempt at a Solution

I have no idea to do this, can someone help?

First, you have to write the equations that express x, y and z in terms of θ, φ and r. Then you write i, j and k in terms of the unit vectors $e_\theta, e_\phi$ and $e_r$. Then you just substitute.

dx said:
First, you have to write the equations that express x, y and z in terms of θ, φ and r. Then you write i, j and k in terms of the unit vectors $e_\theta, e_\phi$ and $e_r$. Then you just substitute.

is the forum having problem with latex?

## What is the formula for converting 3D cartesian coordinates to polar coordinates?

The formula for converting 3D cartesian coordinates (x, y, z) to polar coordinates (r, θ, φ) is:
r = √(x² + y² + z²)
θ = arccos(z/r)
φ = arctan(y/x)

## What is the difference between 3D cartesian coordinates and polar coordinates?

3D cartesian coordinates use x, y, and z coordinates to represent a point in space, while polar coordinates use r, θ, and φ coordinates. The main difference is that polar coordinates use a distance (r) and two angles (θ and φ) to represent a point, while cartesian coordinates use three perpendicular axes.

## What is the range of values for angles in polar coordinates?

Angles in polar coordinates have a range of 0 to 2π (or 0 to 360 degrees). This represents a full rotation around the origin point (r = 0).

## What is the purpose of converting from cartesian to polar coordinates?

Converting from cartesian to polar coordinates can be useful in certain situations, such as when working with circular or spherical objects. It can also make certain calculations, such as finding a point's distance from the origin, easier to visualize and solve.

## How do you convert polar coordinates to cartesian coordinates?

To convert polar coordinates (r, θ, φ) to cartesian coordinates (x, y, z), use the following formula:
x = r sin(θ) cos(φ)
y = r sin(θ) sin(φ)
z = r cos(θ)