Difference Between Scalar and Vector - A Complete Guide

What Is Scalar Quantity?

A scalar quantity is a physical quantity with no direction and no magnitude. Some physical quantities can be defined solely by their numerical value (in their respective units) without regard for directions (they have none).

The sum of these physical quantities is done using basic algebraic procedures. Only their magnitudes are added.

Examples of Scalar Quantities

There are many examples of scalar quantities; some of the more common ones are:

There are several vector quantity instances, some of which are listed below:

• Mass
• Speed
• Distance
• Time
• Area
• Volume
• Density
• Temperature

Also read -

• NCERT Solutions for All Subjects
• NCERT Notes for all subject
• NCERT Exemplar Solutions for All Subjects

What is a Vector Quantity?

A physical quantity with both direction and magnitude is referred to as a vector quantity. And vector meaning in Telugu is వెక్టర్

There are several vector quantities, some of which are listed below:

• Linear momentum
• Acceleration
• Displacement
• Momentum
• Angular velocity
• Force
• Electric field
• Polarization

There are ten main types of vectors that are regularly used in mathematics. The ten types of vectors are as follows:

1. Zero vector
2. Unit Vector
3. Position Vector
4. Co-initial Vector
5. Like and Unlike Vectors
6. Co-planar Vector
7. Collinear Vector
8. Equal Vector
9. Displacement Vector
10. Negative of a Vector

Null Vector or Zero Vector:-

A vector having zero magnitude and no specific direction is termed as zero vector or null vector. It is represented as (0,0) in two-dimensional and $\overrightarrow{0}$.

Example- Vector pointing itself is termed a zero vector.

Unit Vector:-

A vector with magnitude one is termed as a unit vector. The magnitude of the unit vector is always one, and it is represented by a lowercase alphabet with a "hat" circumflex $
\text { "û". }
$ However, two unit vectors cannot be equal because their directions may differ.

Position Vector:-

A position vector is defined as any point X in the plane. It just indicates the current location.

Example- Let OX be a point in a plane that is perpendicular to the origin.

If O is used as the reference origin and X is an arbitrary point in the plane, the vector is referred to as the point's position vector.

Co-initial Vectors:-

It are a type of initial vector that is used in the initialization. When two or more vectors have the same starting point, they are said to be co-initial vectors.

For example, Vectors AB and AC are co-initial vectors since they both have the same starting point A.

Like and Unlike Vectors:-

Vectors with the same directions are called like vectors, while vectors with the opposite directions are called unlike vectors.

Coplanar Vectors:-

Coplanar vectors are three or more vectors that lie in the same plane.

Collinear Vectors:-

Collinear vectors, also known as parallel vectors, are vectors that lie in the same or parallel line with regard to their magnitude and direction.

Equal Vectors:-

When two vectors have the same direction and magnitude, even if their initial locations are different, they are said to be equal vectors.

Displacement Vector:-

If a point is moved from position A to B, the vector AB denotes the displacement vector.

Negative of a Vector:-

If a vector has the same magnitude and direction as another vector, then any vector with the same magnitude but the opposite direction is said to be negative of that vector.

If two vectors a and b have the same magnitude but opposing directions, they may be represented as

a = – b

What is the Difference between Scalar and Vector Quantity?

The following is the scalar quantity and vector quantity difference. In terms of the scalar and vector difference, the following points are crucial:

Here's a brief and simple comparison between scalar and vector quantities:

Definition:

• Scalar Quantity: It only has magnitude (size or amount). Example: temperature, speed.
• Vector Quantity: It has both magnitude and direction. Example: velocity, force.

Representation:

• Scalar: Represented by a single number with a unit (e.g., $5 \mathrm{~m}, 20^{\circ} \mathrm{C}$ ).
• Vector: Represented by an arrow showing direction and length indicating magnitude (e.g., 10 m east).

Examples:

• Scalar: Mass, time, distance, energy.
• Vector: Displacement, acceleration, momentum.

Operations:

• Scalar: It can be added or subtracted directly.
• Vector: It requires vector addition, considering both magnitude and direction.

Effect of Direction:

• Scalar: Direction does not matter.
• Vector: Direction is crucial, changing direction changes the vector.