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Scaler and Vector Quantities Class 11 Physics Chapter 4 CBSE

All the physical quantities are needed to represent two things numerical value and their unit, as example mass of five kilograms is written as 5 kg, so all physical quantities are represented by two terms one is a numerical value and the other is a unit. A physical quantity(P.Q) is the product of a numerical value and its unit. The physical quantities are of two types (i) Scaler Quantity (ii)Vector Quantity

Scaler Quantity: The type of quantity which are needed to represent the magnitude only as example teperature, a room temperature of 5°C gives complete information about the temperature of the room.

Vector Quantity: The vector Quantity is the physical quantity which is needed to represent by the magnitude as well as by the direction,as example, a car is moving towards the west at a speed of 50 km/h, then the given speed with direction is not actually speed,it is a velocity. The speed is the scaler quantity and velocity is the vector quantity.

 Scaler Quantity Vector Quantity Represented by numerical value Represented by the numerical value and direction Two or more similar scaler quantities are added according to the ordinary rule of algebra These are added according to the vector law of addition It is one dimensional It is multi-dimensional Its quantity changes as the magnitude changes Its quantity changes as the magnitude and direction changes Examples are speed, mass, temperature, time etc Examples are velocity,weight,dislacement,force etc

Why does Current as well as Pressure have the direction but these are not vector quantity?

Current and pressure don’t follow the law of vector addition as an example if 2A and 5A currents are flowing through two wires,if both wires are connected to the same wire the current on the later wire is always 2+5=7A, and the resultant of both will not change with the changing angle between both the wires, similarly in case of the two pressure values are directed to a point then the resultant will be scaler sum of both and will not change with the angles between both pressure values.

Representation of the vector quantity:Let a physical quantity A act in a particular direction,then it is represented by $\fn_cm \overrightarrow{A}$

$\fn_cm \overrightarrow{A}$ shows the magnitude of A with the direction while

$\fn_cm \left | \overrightarrow{A} \right |$  shows the magnitude of vector A in short mod A, sometimes also can be written simply A

Representation of the vectors:

The vector (A) 5 m/s  30° north of east is represented as follows

$\fn_cm \overrightarrow{A}$ = 5 m/s  30° north of east

Important Points related to Vectors:

(i) On rotating 2π  radian vector doesn’t change.

(ii)A vector can shift parallel to itself,it is known as parallel shifting of the vector provided its size is same.

(iii)The angle between two vectors is the smaller of two angles between the vectors when they are joined tail to tail ,0°≤θ≤180°

The angle between two vectors can’t be more than 180°

The angle between two vectors is the angle between them when connected tail to tail

In the first figure the angle between A and B is  120° but in the second figure the angle between A and B is 60°

Types of the vectors:

Equal vectors: Two vectors of the same physical quantities are called equal vectors when their magnitudes are equal

Let we have two vectors $\fn_cm \overrightarrow{A}$  and $\fn_cm \overrightarrow{B}$ such that

$\fn_cm \overrightarrow{A}$ = 1 m/s east and $\fn_cm \overrightarrow{B}$= 1m/s west

The vector A and Vector B are not equal because their magnitudes are the same but directions are different

So we can say

$\fn_cm \left | \overrightarrow{A} \right |=\left | \overrightarrow{B} \right |$

$\fn_cm \overrightarrow{A}\neq \overrightarrow{B}$

If  $\fn_cm \overrightarrow{A}$ = 1 m/s east and $\fn_cm \overrightarrow{B}$= 1m/s east

Here vector A and vector B are equal because their magnitude and directions are the same,therefore

$\fn_cm \left | \overrightarrow{A} \right |=\left | \overrightarrow{B} \right |$

Negative of a vector: When the magnitudes of the two vectors are same but their directions are opposite to each other then they are negative of each other.

Let there are two vectors $\fn_cm \overrightarrow{A}$ and $\fn_cm \overrightarrow{B}$, vector A  is equal to vector B in magnitude but have opposite directions ,as an example

If  $\fn_cm \overrightarrow{A}$ = 1 m/s east and $\fn_cm \overrightarrow{B}$= 1m/s west

$\fn_cm \left | \overrightarrow{A} \right |=\left | \overrightarrow{B} \right |,\overrightarrow{A} =-\overrightarrow{B}$

Parallel and Antiparallel Vectors: Two vectors which has 0° angle between them are known as parallel vectors and two vectors which has 180° between them are known as antiparallel vectors.

Collinear and Coplaner vectors:The vectors which lies on the same line or same path are known as collinear vectors and the vectors which lies on the same plane.

Two vectors always lie on the same plane means they are always coplaner

Three vectors may be coplanar or non coplanar

Concurrent Vectors: Two or more vectors intersecting at the same point or two or more than two vectors whose lines of actions intersects at the common point are known as concurrent vectors.

As an example 2 or more forces acts on an object are concurrent vectors.

Unit Vector:A vector whose magnitude is 1 known as init vector,unit vector is very important for resolving many problems in physics of vectors.

$\fn_cm \left | \hat{A} \right | =1$

A unit vector is represented by $\fn_cm \hat{A}$,a unit vector shows the direction of a vector.

A unit vector is evaluated as follows

$\fn_cm \hat{A}=\frac{\overrightarrow{A}}{\left | \overrightarrow{A} \right |}$

Null Vector or Zero Vector: The vector which is of 0 magnitudes and has an arbitrary direction

Circular Motion: Angular velocity and angular displacement

Electronic Configuration of s,p and d orbitals

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