Difference Between Vectors and Scalars

Vectors vs Scalars

In science, quantities that refer to physical properties of a phenomena or a substance and can be quantified are called physical quantities. For example, the velocity of a traveling vehicle, the length of a piece of wood and the luminosity of a star are all physical quantities. Such physical quantities can be divided in to two main categories: namely, vectors and scalars.

What is a vector?

A vector is a physical quantity having both, a magnitude and a direction. For example, a force acting on a body is a vector. Displacement of an object is also a vector since the distance in a specific direction is taken into account when calculating the displacement.

Two vectors are equal when they have the same magnitude and direction. For example, assume two vehicles, one moves with a speed of 30 km/h towards North, and another vehicle moves with a speed of 30 km/h towards West. Then the velocities of the two vehicles are not equal, since the direction of the velocity vector is not the same. Had both the vehicles moved towards North then the velocities would have been the same.

Vectors can be represented using directed straight line segments with length proportional to the magnitude. It is possible to add vectors of the same type using triangle law and polygon law; i.e. it is possible to add two velocities, but it is impossible to add a force to a velocity.

What is a scalar?

A vector is a physical quantity having a magnitude but no direction. For example, volume of an object, temperature of a point in space, and work done to accelerate a vehicle are all scalars, since none of them is characterized by a direction. Therefore, equality of scalars is defined from magnitude only.

If two scalars have the same magnitude and they are of the same type then the two scalars are equal. In the previous example, the speed (a scalar) of both vehicles is 30 km/h. Hence, the two scalars are equal. Since scalars are just numerical values, two scalars of the same type are added together just like real numbers. For example, if 2 liters of water is added to 3 liters of water, then we get 2 + 3 = 5 liters of water.

What is the difference between a vector and a scalar?

• Vectors have both, a magnitude and direction, but scalars have magnitude only.

• Vector equality occurs only when both the magnitude and the direction of two vectors of the same type are the same, but in the case of scalars, equality of magnitude is sufficient.

• Scalars of the same type can be added just as real numbers, but the addition of vectors should be done using the polygon law.