- #1
tekness
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I would like to know how to perform a cross product on polar coordinates.
Thank You
Thank You
tekness said:I would like to know how to perform a cross product on polar coordinates.
Thank You
tiny-tim said:Hi tekness!
Can you give us an example of two vectors you're trying to cross-product?
tekness said:I am just looking for a general way to perform the operation. I will perform a cross product between E and H fields that are in polar coordinates. I don't want to go through the hassle of converting back and forth :).
tekness said:so for example.
I haveCode:|i j k| |rcos() rsin() Z1| |r2cos()2 r2sin()2 Z2|
the 2 is for a different value/angle.
So just perform the same cross product operation as rectangular coordinates would require?
In polar coordinates, the cross product is a mathematical operation that results in a vector perpendicular to the two vectors being multiplied. It is commonly used in 3-dimensional space and can be calculated using the determinant of a 3x3 matrix.
The cross product in polar coordinates can be calculated by multiplying the magnitudes of the two vectors being multiplied, multiplying the sine of the angle between them, and calculating the direction using the right-hand rule. This can also be represented using the cross product formula: A x B = |A||B|sin(theta)n, where theta is the angle between the two vectors and n is the unit vector in the direction of the cross product.
Polar coordinates are useful for representing vectors that have both magnitude and direction. In a cross product, polar coordinates can help determine the direction of the resulting vector, as well as the angle between the two vectors being multiplied.
Cross products in polar coordinates are commonly used in physics, engineering, and computer graphics. They can be used to calculate torque, angular momentum, and magnetic fields, among other things. In computer graphics, they are used to determine the orientation of objects in 3-dimensional space.
One limitation of using polar coordinates in a cross product is that it is only applicable in 3-dimensional space. Additionally, the cross product can only be calculated between two vectors, so it cannot be used to multiply more than two vectors at a time. Lastly, the direction of the resulting vector can only be determined up to a sign, so it is not possible to determine the exact direction using polar coordinates alone.