Final answer:
The magnitude of a vector cannot be negative because magnitudes are scalar quantities that are always positive. Velocity can have a negative value, but this refers to its direction, not its magnitude. Magnitudes are used to indicate size or length, and cannot be negative by definition.
Step-by-step explanation:
The magnitude of a vector cannot be negative because magnitudes are scalar quantities that represent the size or length of a vector, which is inherently a positive value. Even if a vector has a negative component, the magnitude—being the absolute value of the vector—is always positive. This can be seen in an equation where if a scalar a is negative in a vector equation, the magnitude of the resultant vector is determined by the absolute value of a. Therefore, the answer to the question 'Can a magnitude of a vector be negative?' is b) No.
Furthermore, in physics, certain conventions dictate whether a vector is considered to have a negative or positive direction. For example, by convention, a downward-moving object may be assigned a negative sign (-). However, this is indicative of direction, not magnitude.
It's also important to understand the difference between vectors and scalars. While velocity is a vector quantity that includes both magnitude and direction, therefore it can have a negative value signifying direction, the magnitude of this velocity, which is speed, would be a scalar and thus always a positive quantity.