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gsingh2011
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Did someone just realize that taking the determinant of a specific matrix gives you the cross product formula, or is there is a specific conceptual reason why it works?
gsingh2011 said:Did someone just realize that taking the determinant of a specific matrix gives you the cross product formula, or is there is a specific conceptual reason why it works?
The cross product in determinant form is a mathematical operation that takes two vectors in three-dimensional space and produces a vector that is perpendicular to both of the original vectors.
The cross product using the determinant form is calculated by taking the determinant of a 3x3 matrix that is composed of the unit vectors in the x, y, and z directions and the components of the two vectors being crossed.
The cross product in determinant form has many applications in physics and engineering, including calculating torque, finding the direction of a magnetic field, and determining the normal vector to a plane.
No, the cross product in determinant form is only defined for vectors in three-dimensional space. In higher dimensions, the cross product is replaced by the concept of a wedge product.
The cross product and the dot product are both operations on vectors, but they have different properties and produce different results. The cross product produces a vector, while the dot product produces a scalar. Additionally, the cross product is only defined for three-dimensional vectors, while the dot product can be calculated for any number of dimensions.