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## Homework Statement

I need to convert this to a polar coordinate

[tex] \vec{F} = 5xz\vec{i} + 5yz\vec{j} + 4z^3\vec{k} [/tex]

## Homework Equations

## The Attempt at a Solution

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

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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.

- #1

- 564

- 1

I need to convert this to a polar coordinate

[tex] \vec{F} = 5xz\vec{i} + 5yz\vec{j} + 4z^3\vec{k} [/tex]

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

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- #2

Homework Helper

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dx said:

is the forum having problem with latex?

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)

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.

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).

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.

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)

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