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Vector products, also known as cross products, are a binary operation on two vectors in three-dimensional space. The result of the cross product is a vector that is perpendicular to both of the original vectors. This operation is fundamental in various fields, including physics, engineering, and computer graphics.

The cross product of two vectors A and B, denoted as A × B, is defined as a vector C such that:

C = |A||B|sin(θ) n

where |A| and |B| are the magnitudes of vectors A and B, θ is the angle between A and B, and n is a unit vector perpendicular to the plane containing A and B. The direction of n is determined by the right-hand rule.

The cross product has several important properties. It is not commutative, meaning A × B is not equal to B × A. Instead, A × B = - (B × A). The cross product is also distributive over vector addition, meaning A × (B + C) = A × B + A × C.

The magnitude of the cross product vector is equal to the area of the parallelogram spanned by the two vectors. This property is useful in calculating areas and volumes in three-dimensional space.

In summary, vector products, or cross products, are a crucial operation in three-dimensional vector mathematics. They provide a way to find a vector perpendicular to two given vectors and have applications in various scientific and engineering disciplines.