Vector and Scalar Quantity

Vector and Scalar Quantity

Physical quantities are two types ￫🏇

• Scalar Quantity
• Vector Quantity

Scalar Quantities

There are some physical quantities which have only magnitude, they do not have any direction.

For example mass, distance, time, speed, pressure, volume, work, energy, power, charge, electric-current, temperature, specific heat, etc. These types of Quantities are called Scalar Quantities.

Certain Scalar quantities are completely described by a numerical values or by single physical quantity and there addition, subtraction, multiplication, and division according to a ordinary rules of algebra. For example If two bodies having of mass 300 kg and the other having a mass of 150 kg, then the result according to a ordinary rules of algebra is 450 kg.

Vector Quantities

There are some physical quantities which have magnitude along with direction and which follow Vector rule of addition(vector are added by geometrical rules) are called Vector Quantities.

For example Displacement, position, acceleration, force, momentum, electric field, magnetic field, etc. Such types of quantities are called Vector Quantities.
It is also necessary to mention magnitude along with the direction of describing vector quantities for any vector quantity. Acceleration of a particle is a vector quantity, where the magnitude of a particle shows us how fast a particle increases or decreases its velocity. But the description of a particle is still incomplete because it dose not shows us the direction of a particle. Because of which we can not tell whether acceleration is rising or decreasing. Therefore it is necessary to describe the direction in acceleration.
If there is a physical quantities which is a vector. then it is necessary to have direction in it. But if there is a direction in a physical quantity, its vector is not necessary. it can also be a scalar.

Position Vector And Displacement Vector

Position Vector

The Position vector expresses the position of a moving object. To express the position of a moving object, at the convenience, assuming a point as the original point, expresses the position of moving  objects relative to it. 
Suppose a particle is at point P in space, having coordinate (x,y) with respect to the origin O (0,0). Then the vector  having O and P as its initial and final points, respectively, is called the position vectors of the particle P with respect to O. it is represented by  where || = Which represent the distance between O to P, again at time t2  particle reaches at point Q. This time the position vector of  is . If we connect the points P to Q, then the displacement vector at at time interval t2 - t1.

Displacement Vector

The shortest distance between the initial and final position vector of the particle.

Vectors and Notation system

Any vector quantity can be represented by an arrow. This arrow (→) is called vector. Where the length of an arrow indicates the magnitude and the direction can be denoted by arrowheads.

For example  suppose a particle travel 20 km/sec  velocity at east and the Other Particle travel 40 km/sec vector North-south For this we assumed 10 km/sec = 1 cm velocity. Therefore, the velocity of particle A is 2 cm and particle B is 4 cm.

Vector quantities are represented by Bold black letters with arrow. e.g. If there is a vector A is denoted by .

Types of Vectors

1. Equal vectors Two or more vectors are said to be equal if there magnitude and direction are equal are called Equal Vectors.
2. Opposite Vector Two or more vectors are said to be opposite if there magnitude are equal but the directions are opposite are called Opposite Vectors.
3. Unit vector A vector Whose magnitude is unity is called a Unit Vector. The unit vector is the direction of a given vector.