# Cross product in non-cartesian coordinates?

• moonman
In summary, the cross product of two vectors in cylindrical coordinates can be found by representing the vectors in terms of perpendicular components or knowing the angle between them. The basis for representing the vectors does not affect the calculation.
moonman
How do you go about crossing two vectors if they are in cylindrical coordinates? I have one vector in the direction of R and another in the direction of theta. Can this be done?

Certainly.

Daniel.

moonman said:
How do you go about crossing two vectors if they are in cylindrical coordinates? I have one vector in the direction of R and another in the direction of theta. Can this be done?

Two vectors (non-parallel) lie in a plane. The cross product is always a vector perpendiculat to that plane. When the two original vectors are perpendicular, the magnitude of the cross product is the product of the magnitutes. The basis for representing the vectors does not change this. As long as you represent the vectors in terms of perpendicular components, or if you know the angle between them, the cross product can be determined.

## 1. What is the cross product in non-Cartesian coordinates?

The cross product is a mathematical operation that produces a vector perpendicular to two given vectors. In non-Cartesian coordinates, the cross product is calculated using the same formula as in Cartesian coordinates, but with the vectors expressed in terms of non-Cartesian basis vectors.

## 2. What is the significance of the cross product in non-Cartesian coordinates?

The cross product is useful in non-Cartesian coordinates because it allows us to find a vector that is perpendicular to two other vectors. This is important in many applications, such as calculating torque and angular momentum in physics and engineering.

## 3. How is the cross product calculated in non-Cartesian coordinates?

The cross product in non-Cartesian coordinates is calculated using the determinant of a matrix formed by the basis vectors and the components of the two given vectors. The resulting vector is a linear combination of the basis vectors and represents the cross product in the non-Cartesian coordinate system.

## 4. Can the cross product be applied to any type of non-Cartesian coordinate system?

Yes, the cross product can be applied to any type of non-Cartesian coordinate system, as long as the basis vectors are orthogonal (perpendicular) to each other. Examples of non-Cartesian coordinate systems include cylindrical and spherical coordinates.

## 5. What are some real-world examples of using the cross product in non-Cartesian coordinates?

The cross product in non-Cartesian coordinates is used in a variety of fields, including physics, engineering, and computer graphics. Some examples include calculating the torque on a spinning object, determining the direction of the magnetic field around a wire, and generating 3D animations in computer graphics.

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