Question

In physics, quantities are classified as either scalars or vectors. What property or properties completely describe a vector quantity?

Hint:

Think of displacement compared to distance. Displacement needs a size and a direction to be fully specified, while distance needs only a size.

Answer 1

Step 1: Unlike a scalar, a vector quantity is one for which direction genuinely matters, not just size.

Step 2: A vector quantity is completely described only when we state both its magnitude, meaning how large it is, and its direction, meaning which way it acts or points.

Step 3: For example, saying a car has a velocity of 60 kilometre per hour is not a complete description of its velocity, because velocity is a vector. We must also give the direction, such as 60 kilometre per hour due north, for the description to be complete. The same is true of displacement, force, and acceleration.

Step 4: Because direction is part of the definition, vector quantities cannot be added using plain arithmetic addition. Instead they are combined using vector addition rules, such as the triangle law or the parallelogram law, which take the directions of the individual vectors into account. For example, a force of 3 newton acting north and a force of 4 newton acting east do not add up to 7 newton, they add up to 5 newton acting in a direction between north and east, found using the parallelogram law.

So a vector quantity is completely described only by stating both its magnitude and its direction together.