Which of the following best describes the difference between a scalar and a vector quantity?

• A. A vector is always larger in value than a scalar.
• B. A scalar has both magnitude and direction, while a vector has only magnitude.
• C. A scalar has only $\mathrm{magnitude}$, while a vector has both $\mathrm{magnitude}$ and $\mathrm{direction}$.
• D. A scalar can be $-$negative, but a vector cannot.

Answer: (C)

Verified step by step guidance

1. Understand the definitions: A scalar quantity is described by only its magnitude (size or amount), such as temperature or mass.
2. Recognize that a vector quantity has both magnitude and direction, such as velocity or force.
3. Note that the difference is not about size or value, but about the presence or absence of direction.
4. Remember that scalars can be positive or negative depending on the context (e.g., temperature), and vectors can also have negative components depending on their direction.
5. Therefore, the key distinction is that scalars have only magnitude, while vectors have both magnitude and direction.