Which product of two vectors gives a vector that is perpendicular to the initial vectors in three-dimensional space?

The cross product of two vectors in three-dimensional space results in a new vector that is perpendicular to both of the original vectors. This property arises from the definition of the cross product, which produces a vector that follows the right-hand rule.

When you take the cross product of vectors A and B, the resulting vector ( \mathbf{C} = \mathbf{A} \times \mathbf{B} ) is orthogonal to the plane formed by vectors A and B. This is particularly significant in physics and engineering, where understanding directions and forces is crucial.

In contrast, the dot product provides a scalar value and does not produce a perpendicular vector. The scalar product also refers to the same operation as the dot product, emphasizing its nature as a single value rather than yielding a vector. A normal vector is a concept related to perpendicularity but does not describe a specific vector obtained from two vectors through a product. Therefore, the cross product is the definitive method to calculate a vector that is perpendicular to the given vectors in three-dimensional space.