Which of the following quantities is necessary to define a vector?

Which of the following quantities is necessary to define a vector?

• A. Mass
• B. Direction and speed
• C. Magnitude and direction
• D. Volume and velocity

Answer: (C)

In physics, a vector is a quantity that has both magnitude and direction. The magnitude refers to how much of the quantity is present, while the direction indicates where that quantity is pointing. For example, one can describe a displacement vector by stating that an object moves 5 meters to the east; here, the "5 meters" is the magnitude, and "east" is the direction. The other options do not fully define a vector. Mass is a scalar quantity that has only magnitude and no direction. Direction and speed describes a relationship similar to velocity, but it lacks the explicit mention of magnitude which makes it incomplete for defining a vector. Volume and velocity are also a mix of scalar and vector quantities: volume is scalar with magnitude only, while velocity encompasses direction and magnitude, similar to what is required for a vector but does not directly qualify as defining one alone. Thus, the most accurate choice for defining a vector is indeed the combination of magnitude and direction.

In physics, a vector is a quantity that has both magnitude and direction. The magnitude refers to how much of the quantity is present, while the direction indicates where that quantity is pointing. For example, one can describe a displacement vector by stating that an object moves 5 meters to the east; here, the "5 meters" is the magnitude, and "east" is the direction.

The other options do not fully define a vector. Mass is a scalar quantity that has only magnitude and no direction. Direction and speed describes a relationship similar to velocity, but it lacks the explicit mention of magnitude which makes it incomplete for defining a vector. Volume and velocity are also a mix of scalar and vector quantities: volume is scalar with magnitude only, while velocity encompasses direction and magnitude, similar to what is required for a vector but does not directly qualify as defining one alone. Thus, the most accurate choice for defining a vector is indeed the combination of magnitude and direction.