Final answer:
In mathematics, the term 'product' refers to either a scalar product (dot product) or a vector product (cross product), with the scalar product resulting in a scalar and the vector product resulting in a vector that is perpendicular to the plane containing the original vectors.
Step-by-step explanation:
In mathematics, particularly when dealing with vectors, the term product can refer to either a scalar product (dot product) or a vector product (cross product).
Scalar Product (Dot Product)
The scalar product is the result of the multiplication of two vectors that yields a scalar value. This operation involves multiplying the magnitudes of the two vectors along with the cosine of the angle between them and is denoted by placing a dot between the two vectors (A · B).
Vector Product (Cross Product)
The vector product is a vector resulting from the multiplication of two vectors, denoted by placing a cross between them (A × B). The result is a vector that is perpendicular to the plane containing the original vectors. Its magnitude is given by the product of the magnitudes of the two vectors and the sine of the angle between them (AB sin θ).
Understanding these products is crucial for physical applications. In physics, for instance, the impulse is proportional to the product of force and time interval, while torque is defined as a vector product involving force and its distance from a pivot.