In physics, scalars are quantities which are determined uniquely by a number and units. A scalar has a magnitude but no direction. Length, mass, temperature, speed, time, area, volume, density, and energy are examples of scalar quantities.

There are other quantities called vectors which can’t only be defined by one number. Vectors are quantities that are useful to describe physical quantities that have both a magnitude and direction associated with them. For instance, in one dimensional motion, velocity has a certain magnitude, which is speed, and a direction. Velocity, acceleration, displacement, force, momentum and torque are examples of vector quantities.

Vector has a magnitude and direction and that is why it’s represented by an arrow. The arrow is always drawn so that its direction is same with the direction of the vector it represents. The length of the arrow is drawn proportional to the magnitude of the vector.

The figure below shows a car travelling on a road. The arrow represents the velocity vector at each position.

Scalar and Vector Quantities in Physics

Equality of Vectors

Two vectors are equal (\({\vec{A}}={\vec{B}}\)) if they satisfy the following conditions:

  • |A|=|B| (Magnitude)
  • Directions are equal
  • Location and starting point do not matter
  • Units are same

Additional Resources