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moonman
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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?
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?
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.
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.
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.
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.
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.