Question

Which of the following is a vector: a person’s height, the altitude on Mt. Everest, the age of the Earth, the boiling point of water, the cost of this book, the Earth’s population, the acceleration of gravity?

Short answer

Acceleration due to gravity is only a vector quantity.

Step-by-step solution

Vector definition

A quantity that has both magnitude and direction is known as a vector. Some examples of the vector quantity are displacement, velocity, force, torque, etc.

Vector quantity

A person’s height is measured in inches and is independent of direction; thus, it is a scalar quantity.

The altitude of Mt. Everest is measured in meters and is independent of direction; thus, it is a scalar quantity.

The age of the Earth is measured in years and is independent of direction; thus, it is a scalar quantity.

The boiling point of water is 100°C and is independent of direction; thus, it is a scalar quantity.

The cost of this book is measured in currency and is a fixed number; thus, it is a scalar quantity.

The Earth’s population may change, but there is no direction of its movement; thus, it is a scalar quantity.

The acceleration due to gravity may be positive (for an object moving towards the center of the planet) and negative (for an object moving away from the planet's center), depending on its direction; thus, it is a vector quantity.

Hence, the acceleration due to gravity is the only vector quantity.