Which of the following statements about $vectors$ and $scalars$ is true?

• A. Both $vectors$ and $scalars$ have direction but only $vectors$ have magnitude.
• B. A $vector$ has both magnitude and direction, while a $scalar$ has only magnitude.
• C. A $scalar$ has both magnitude and direction, while a $vector$ has only magnitude.
• D. Neither $vectors$ nor $scalars$ have direction.

Answer: (B)

Verified step by step guidance

1. Understand the definitions: A scalar quantity is defined as having only magnitude (size or amount) without any direction, such as temperature or mass.
2. Recognize that a vector quantity has both magnitude and direction, such as velocity or force.
3. Compare the properties: Scalars do not have direction, while vectors always have direction associated with their magnitude.
4. Identify the correct statement: Since vectors have both magnitude and direction, and scalars have only magnitude, the true statement is that a vector has both magnitude and direction, while a scalar has only magnitude.
5. Conclude that any statement claiming scalars have direction or that vectors lack direction is incorrect.