In this section, we explore how multiplying a vector by a real number affects its properties. When a vector A is multiplied by a positive scalar λ (λ > 0), the magnitude of the resulting vector |λA| becomes λ times the magnitude of A, while the direction remains unchanged. Conversely, multiplying A by a negative scalar, such as -λ, yields a vector with an opposite direction and the same scaling effect on the magnitude. Additionally, when the scalar has its own physical dimension, the resultant vector will inherit dimensions from both itself and the scalar. An example to illustrate is multiplying a constant velocity vector by time, which results in a displacement vector, showcasing the practical application of this concept in physics. Understanding these principles is essential for further discussions on vector operations and transformations in multi-dimensional motion.