The correct option is **C. Displacement**. ### Explanation of Why Displacement is a Vector 1. **Definition of a Vector**: A vector is a quantity that has both magnitude (size) and direction. This means that to fully describe a vector, you need to specify how much there is (the magnitude) and where it is pointing (the direction). 2. **Understanding Displacement**: Displacement is defined as the change in position of an object. It is a vector quantity because it not only tells you how far an object has moved (the magnitude) but also in which direction it has moved from its initial position to its final position. For example, if an object moves from point A to point B, the displacement is the straight line from A to B, along with the direction of that line. 3. **Mathematical Representation**: Displacement can be represented mathematically as: \[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \] If the initial position is at the origin (0,0) and the final position is at (3,4), the displacement vector can be represented as: \[ \text{Displacement} = (3 - 0, 4 - 0) = (3, 4) \] This indicates a movement of 3 units in the x-direction and 4 units in the y-direction. ### Why the Other Options are Incorrect - **A. Temperature**: Temperature is a scalar quantity. It only has magnitude (e.g., 25 degrees Celsius) and does not have a direction. You can say it is hot or cold, but you cannot say it is "hot to the north" or "cold to the east." Therefore, it does not meet the criteria for a vector. - **B. Speed**: Speed is also a scalar quantity. It measures how fast an object is moving but does not provide any information about the direction of that movement. For example, saying a car is traveling at 60 km/h tells you how fast it is going, but not where it is headed. Thus, speed is not a vector. - **D. Mass**: Mass is another scalar quantity. It measures the amount of matter in an object and is expressed in units like kilograms (kg). Mass does not have a direction; it simply tells you how much matter is present. Therefore, it is not a vector. ### Summary of Key Points - **Displacement** is a vector because it has both magnitude and direction. - **Temperature**, **Speed**, and **Mass** are scalar quantities; they only have magnitude and no direction. - Understanding the difference between vector and scalar quantities is crucial in physics, as it affects how we analyze and solve problems involving motion and forces. ### Revision Summary - Vectors have both magnitude and direction; scalars have only magnitude. - Displacement is a vector quantity representing the change in position. - Temperature, speed, and mass are scalar quantities with no directional component. - Always remember to check if a quantity requires direction to determine if it is a vector.