**Correct Option: C. Force** ### Detailed Explanation To determine which of the given quantities is a vector, we first need to understand the difference between scalar and vector quantities: - **Scalar quantities** are defined by a magnitude (size) only. They do not have a direction associated with them. Examples include temperature, distance, and mass. - **Vector quantities**, on the other hand, have both a magnitude and a direction. This means that in addition to how much there is of something, we also need to know which way it is pointing. Examples include force, velocity, and displacement. Now, let's analyze each option: **A. Temperature** - Temperature is a measure of the average kinetic energy of the particles in a substance. It is expressed in degrees (Celsius, Fahrenheit, Kelvin) and has no direction associated with it. Therefore, temperature is a scalar quantity. **B. Distance** - Distance measures how much ground an object has covered during its motion, regardless of its starting or ending point. It is a non-directional measure and is expressed in units such as meters or kilometers. Thus, distance is also a scalar quantity. **C. Force** - Force is defined as an interaction that causes an object to change its velocity (which includes starting, stopping, or changing direction). It is measured in newtons (N) and has both a magnitude (how strong the force is) and a direction (which way the force is applied). For example, a force of 10 N to the east is different from a force of 10 N to the west. Therefore, force is a vector quantity. **D. Mass** - Mass is a measure of the amount of matter in an object and is expressed in kilograms (kg). It does not have a direction; it only has magnitude. Thus, mass is a scalar quantity. ### Summary of Why Other Options are Incorrect - **Temperature (A)**: Scalar; no direction. - **Distance (B)**: Scalar; no direction. - **Mass (D)**: Scalar; no direction. ### Common Pitfalls - Students often confuse scalar and vector quantities. A common mistake is to think that any physical quantity that can be measured is a vector, but direction is a key distinguishing feature. - Remember that while some quantities can be represented as vectors in certain contexts (like velocity being a vector derived from distance over time), the fundamental definitions of the quantities themselves matter. ### Formulas and Concepts - **Force (F)**: The formula for force is given by Newton's second law of motion: \[ F = m \cdot a \] where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration. This formula highlights that force is dependent on both mass and acceleration, both of which are scalar quantities, but the resulting force is a vector due to its directional nature. ### Revision Summary - **Vector quantities** have both magnitude and direction (e.g., force). - **Scalar quantities** have only magnitude (e.g., temperature, distance, mass). - **Force** is a vector because it involves direction in addition to magnitude. - Always check if a quantity has a directional component to determine if it is a vector.