The vector product, also known as the cross product, is a mathematical operation that takes two vectors and produces a third vector that is perpendicular to both. This operation is commonly used in physics and engineering to find quantities like torque and angular momentum. The magnitude of the resulting vector is determined by the area of the parallelogram formed by the two original vectors. To calculate the vector product, you can use the formula: A × B = |A| |B| sin(θ) n, where A and B are the original vectors, θ is the angle between them, and n is a unit vector in the direction of the resulting vector. The vector product is only defined in three-dimensional space and is represented in coordinate form using the determinant of a matrix.