# Difference between vector and scalar

By John

Every scientific explanation can be explained with the help of a number of physical quantities each expresses a special meaning and significance in that context. According to the definition, a physical quantity is the measurable and quantifiable physical property that carries unique information with it. Based on the dependency of direction, physical quantities can be classified into two categories — scalar and vector. Both these quantities are in use to represent the motion of an object. Let us now discuss what is the difference between scalar and vector

What is Scalar?
The quantity, which has only magnitude and no direction, is termed as a scalar quantity. For example length, mass, speed, etc are some of the examples of scalar.

What is a Vector?
The physical quantity, which comprises of both magnitude and direction, is termed as a vector quantity. For example, velocity, momentum, force, etc are some of the examples of scalar.

The important difference between scalar and vector:

Parameters Scalar Vector
Meaning A scalar quantity has only magnitude, but no direction. Vector quantity has both magnitude and direction.
Quantities Every scalar quantity is one-dimensional. Vector quantity can be one, two or three-dimensional.
Change It changes with the change in their magnitude It changes with the change in their direction or magnitude or both.
Resolution Scalar quantity cannot be resolved as it has exactly the same value regardless of direction. Vector quantity can be resolved in any direction using the sine or cosine of the adjacent angle.
Operation Any mathematical operation carried out among two or more scalar quantities will provide a scalar only. However, if a scalar is operated with a vector then the result will be a vector. The result of mathematical operations between two or more vectors may give either scalar or vector. For example, the dot product of two vectors gives only scalar; while, cross product, summation, or subtraction between two vectors results in a vector.
Expression They are denoted by simple alphabets, e.g. V for velocity. They are denoted by boldface letters, e.g. V for velocity or putting an arrowhead over the letter.
Measurement Simple Complex
Example A car is moving at a speed of 30 Km per hour. A car is moving with a velocity of 30 Km per hour in the East.