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kidsasd987
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Is this just a coincidence that cross product can be found from determinant of 3*3 matrix? what is the differences between wedge product and cross product?Thanks.
No.Is this just a coincidence that cross product can be found from determinant of 3*3 matrix?
https://www.physicsforums.com/threads/wedge-product-cross-product.117231/what is the differences between wedge product and cross product?
The cross product, also known as the vector product, is a mathematical operation that takes two vectors and produces a third vector that is perpendicular to both of the original vectors. It is denoted by a × b and is defined as |a| |b| sinθ n, where |a| and |b| are the magnitudes of the two vectors, θ is the angle between them, and n is a unit vector perpendicular to the plane containing a and b.
The cross product can be calculated using the following formula: a × b = (ay bz − az by)i + (az bx − ax bz)j + (ax by − ay bx)kwhere i, j, and k are the unit vectors in the x, y, and z directions, respectively.
The cross product has several applications in mathematics, physics, and engineering. It is commonly used to calculate the torque on an object, determine the direction of a magnetic field, and find the normal vector to a plane. It is also used in 3D graphics and computer vision to calculate lighting and shading effects.
The determinant of a matrix is a numerical value that is calculated from the elements of the matrix. It is denoted by det(A) or |A| and is used to determine various properties of the matrix, such as whether it is invertible or singular, and to solve systems of linear equations. The determinant is equal to the sum of the products of the elements in each row or column of the matrix, multiplied by their respective cofactors.
The determinant of a matrix can be calculated using various methods, such as expansion by minors, row reduction, or using the Leibniz formula. One common method is the Gaussian elimination method, which involves performing elementary row operations on the matrix until it is in upper triangular form. The determinant is then equal to the product of the elements on the main diagonal of the upper triangular matrix.