Vector multiplication refers to the operation of combining two vectors to produce a new vector or a scalar. There are two primary types of vector multiplication: the dot product and the cross product. The dot product results in a scalar value and measures the extent to which two vectors point in the same direction, while the cross product produces a new vector that is perpendicular to the plane formed by the original vectors. In the dot product, the multiplication involves the magnitudes of the vectors and the cosine of the angle between them. In contrast, the cross product uses the magnitudes of the vectors and the sine of the angle, resulting in a vector whose direction is determined by the right-hand rule. Both operations are fundamental in fields such as physics and engineering, where they help describe forces, motion, and other vector-related phenomena.