# Is Force A Vector Quantity: Why, How, Proof And Detailed Facts

Force is a vector quantity, and its S. I. Unit is Newton.

To be a vector quantity, one should have direction as well as magnitude. As force has both direction and magnitude, it is a vector quantity.

Is force a vector quantity? Absolutely, it is a vector quantity. It is evident that each and every quantity has magnitude. But, in this case, it would be very confusing if one does not know the direction, it would be impossible to solve the puzzle. And hence, the force has both magnitude as well as direction. Thus, it is a vector quantity.

## What is Force?

Force is an external factor responsible for changing the state of the body.

It would either push the body to get it into motion, or stop it from being in motion; it can work both ways. The famous Greek philosopher Aristotle said that force causes “unnatural motion.”

As force is a vector quantity, it is denoted with an arrow above it as:

The formula for deriving force is given as: F = m.a

Force’s S. I. Unit is Newton (N) or kg. m / s2.

Dimensions of force are given as: LMT-2

Further, three concepts are related to force. First is Thrust, in which the object’s velocity is increased. Drag, in which the object’s velocity is decreased. And Torque, in which the object’s rotational speed is changed. Pressure can be referred to yet another type of force, and it is the distribution of small forces applied over a body.

There is contact force, which needs physical contact between two objects to occur. Contact forces include some non- fundamental forces, examples of which are given below. Then there are non- contact forces that do not need physical contact between the objects. Non- contact forces include the fundamental forces given below.

There are four elemental types of forces in nature.

1. Gravitational Force – it is a universal force that acts between masses and it is always attractive.
2. Electromagnetic Force – it acts between charged particles and it is ten times more powerful than the gravitational force. It can be attractive or repulsive. Magnetic force is a type of electromagnetic force.
3. Weak Nuclear Force –It appears only in specific nuclear processes like the nucleus’s beta- decay (β- decay). It is more powerful than gravitational force but feeble than the electromagnetic and strong nuclear force.
4. Strong Nuclear Force – it is more potent than all fundamental forces of nature. It holds together protons and neutrons in the nucleus. Electrons do not experience this force.

When fundamental forces interact with each other, as a consequence, non- fundamental forces arise. Some of the non- fundamental forces are:

1. Normal Force – it acts perpendicularly to the surface to which an object contacts.
2. Frictional Force – it is a surface force that defies the movement of an object. It can further be classified into static friction and kinetic friction.
3. Tension – it acts when an object is being pulled by ropes, strings or cables, etc.
4. Elastic Force – it acts when a body returns to its initial shape and size after being stretched. The body is said to be uninfluenced by the force.
5. Stress – it is the force acting per unit area on a body.
6. Centripetal force – it is also called fictitious or pseudo force. The object is obliged to follow a curved path. It tends to pull the object at the centre.
7. Centrifugal force – it too is fictitious or pseudo force. It is the opposite of centripetal force and tends to pull the object away from the centre.

Read more on Types of forces.

## Why Force is a Vector Quantity?

An object should have both magnitude as well as direction to be a vector quantity.

As we learned above, to be a vector quantity, an object should have both magnitude as well as direction, but that is not enough. For being a vector quantity and to prove it mathematically, an object ought to follow the laws of vector addition or subtraction.

As an example, let’s consider a box lying on top of a table, various forces are acting on it. A gravitational force will pull it down and an equal and opposite normal force will pull it up. Now, these forces balance each other, and as a result, the net force will be zero, and we say that the box is not moving.

Now, if we want to move the box, we need to apply some force to it. But on which side? If we say we applied a force of 3 Newton on the box, how will we know where the box moves? Thus, it is necessary to mention the direction. It will make sense if we say that we need to apply 3 Newton force on the right side, making it easier to understand that the box moves in the right direction.

Thus, if we want to move the box to the left side, we push (apply force) on the left side, and if we want to move the box to the right side, we apply force on the right side.

There are many different methods by which vectors can be added or subtracted, which we will study further in this article.

Laws of vector addition include

1. Addition or subtraction of components of a vector
2. Triangular law of vector addition
3. Parallelogram law of vector addition
4. Polygon law of vector addition

First, let us briefly understand the laws of vector addition.

1. Triangular law of vector addition is applied when two vectors are arranged head to tail format.
2. Parallelogram law of vector addition is applied when two vectors are arranged head to head or in the tail to tail format.
3. Addition and subtraction are performed in simple mathematics.
4. Vectors cannot be added or subtracted to scalars and vice versa.
5. Vectors of the exact nature can be added or subtracted. For example, force should be added or subtracted with only force and not with velocity or any other vector.

Read more on Types of External Forces.

## How to Prove Force is a Vector Quantity?

As mentioned above, it should be proven mathematically to show that the force is a vector.

• Addition or subtraction of components of a vector

For the addition or subtraction of a vector, the components of the vector should be added or subtracted.

For example, let below are two vectors.

Then the sum of two vectors will be:

The difference between the two vectors will be:

• Triangular law of vector addition

In this method, the head of one vector is joined to the tail of another vector, and as a resultant, a diagonal is formed, which is the resultant vector. It follows the head- to- tail format.

For example,

Hence,

When one wants to find the angle between vector

, it can be found using the formula:

• Parallelogram law of vector addition

In this method, the tail or head of one vector is joined to the tail or head of another vector, respectively, and a diagonal is formed as a resultant. It follows head- to- head or tail- to- tail format.

Hence, the formula for finding the resultant will remain the same as the triangular law of vector addition. i.e.,

• Polygon law of vector addition

In this method, every side of a polygon will represent a vector. This polygon will be divided into triangles, and with the help of the triangle law of vector addition, it will be easy to calculate all the vectors.

This law is valid for any number of vectors and is always represented in a cyclic order.

## Why is Electric Line of Force a Vector Quantity?

The fictitious lines that illustrate the direction of an electric field are known as the electric lines of force.

The electric line of force is a force, thus, it is a vector quantity. Factually, force is a vector so it clearly makes the electric line of force a vector quantity. Hence, it has both magnitude and direction.

The electric line of force is popularly known as the Electric Field, and it is given as force per unit charge. The S. I. Unit for electric field is Newton per Coulomb (N/C), or sometimes also given as Volts per meter (V/m).

The formula for electric field is given as:

E=F/q

As evident from the picture above, electric field lines are represented by vector arrows. As shown above, if the charge is positive, the lines come out of the charge and if the charge is negative, the lines go into the charge.

If only positive charge is present in space, then it is said that the electric lines of force come out of a positive charge and extend to infinity. Similarly, if only negative charge is present in space, then it is said that the electric lines of force come from infinity to the negative charge.

The lines are shorter when near a charge and longer when away from it. Electric lines of force never intersect each other yet being extremely dense. When the electric lines of force meet the surface of any object, the electric lines of force become perpendicular to the surface. These lines are not visible but experimentally proven.

Hence, with the help of direction, we can signify that positive charges attract negative charges but repel other positive charges. Similarly, negative charges get attracted towards positive charges but repel other negative charges.

Thus, if one wants to describe the electric lines of force, it cannot be done without the help of direction. One can establish if the charge is positive or negative only with the help of direction. Once the unknown charge of the charge is established, one can find the electric field, its strength, electric flux, etc. thus, we can say that the electric lines of force are a vector quantity.