Difference Between Scalar and Vector

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.

Difference between Scalar and Vector

 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.

As we have now understood the difference between scalar and vector, let us now discuss more scalar and vector.

Scalar

A scalar quantity is one that has only magnitude but no direction. So, it is merely a number accompanied by the corresponding unit. For example, length, mass, duration, speed, etc. are scalars, so they have no direction. Scalar has no specific direction of application, in every direction its value will be exactly the same.

The value of the scalar will be exactly the same in all directions. Therefore, every scalar is a one-dimensional parameter. Consequently, any change in scalar quantity reflects only change in magnitude, as no direction is associated with it.

The rules of ordinary algebra can be applied for combining scalar quantities, such that scalars can be added, subtracted, or multiplied, in the same way, as numbers. However, the operation of the scalar quantities with the same measurement unit can be possible. The multiplication of two scalar quantities is known as the dot product.

Vector

A vector quantity has magnitude with the unit and a specific direction. So specifying the direction of action along with its value or magnitude is mandatory while defining or stating a vector quantity. Displacement, weight, force, velocity, etc. are vectors.

In vector, magnitude represents the size of the quantity, which is also its absolute value, while direction represents the side, i.e. east, west, north, south, etc. We express vector quantities in either of the parameters i.e. one-dimensional, two-dimensional, or three-dimensional parameters. Any change in the vector quantity reflects either change in magnitude, change in direction, or change in both.

One can resolve Vector with the help sine or cosine of adjacent angles (vector resolution). A vector quantity follows the triangle law of addition. The vector product of two quantities is said to be the cross product.

FAQs about Scaler and Vector:

Q.1 Why Electric current is not a vector as it has a direction?

Answer: Electric current flows in a direction opposite to the flow of electrons. Current has both magnitudes as well as a direction but it does not follow vector addition. Therefore, it is a scalar.

Q.2 Which type of quantity is forced either a scalar or a vector quantity?

Answer: Force is a vector quantity as we define it by its magnitude as well as direction.

Q3. What is the magnitude of a unit vector?

Answer: The magnitude of a unit vector is unity. A unit vector has no units or dimensions.

References

https://en.wikipedia.org/wiki/Scalar_(physics)

https://en.wikipedia.org/wiki/Vector_(mathematics_and_physics)