Scalar and vector quantities are used in mathematical models of phenomena. Accurate modeling allows people to understand these phenomena. People are helped by better understanding of the world around them.
(vector) times (vector) produces either a vector or a scalar, depending onwhether the vector product or scalar product is performed.(vector) times (scalar) produces a new vector.
Speed is a scalar quantity as it has magnitude, and no direction. Velocity, on the other hand, is a vector quantity as it has both magnitude and direction.