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Physics - 11 Complete Syllabus Notes

Chapter 2 - Vector

Scalar Quantities::
The physical quantities having only one magnitude are called scalar quantities.
eg. distance,speed etc.


Vector Quantities:

The physical quantities having magnitude and direction and obeying the law of vector addition are called vector quntities.
eg: displacement, velocity, etc.

A vector is represented graphically by straight line with arrow head. The length of the straight line represent magnitude and arrow head represent direction.

Terms regarding in vector:

i) Equal Vector:
Those vector are said to be equal vector if they have same magnitude and direction.

ii) parallel vector:
Vector acting in same direction with equal or unequal magnitude are called parallel vector.

iii)Anti-Parallel Vector:
Vector acting in opposite direction are called Anti- Parallel vector.

iv)Colinear Vector:
Vector acting in same line are called collinear vector.

v) Coplaner Vector:
Vector acting in same plane is called coplaner vector.

vi) Unit vector:
A vector having unit magnitude is called unit vector.
In certesian coordinate system x-axis, y-axis and z-axis are represented by i^, j^ and k^ respectively where i ^, j^ and k^ are unit vectors.



Parallelogram Law of Vector Addition

Statement: If two vectors acting at a point are represents at both in magnitude and direction by two adjacent side of parallelogram. Then the diagonal from that point represent their resultant both in magnitude and direction.

Explanation:
Let two vector and are represented at both in magnitude and direction by two adjecent size and of a parallelogram OACB as shown in figure ii) then from parallelogram law of vector addition the diagonal represent their resultant .

Let be the angle between and and be the angle between and .

Magnitude of Resultant:
From C draw perpendicular, CD and OA produced.
In ODC,
OC 2 = OD 2 + CD 2
OC 2 = (OA + AD) 2 + CD 2
R 2 = (P + Q COS ) 2 + (Q Sin ) 2
On solving with R,
we get,


Direction Of Resultant:
In ODC,
=
=



eqn i) represent the magnitude of resultant and eqn ii) represent the direction of resultant with .

Special Cases:

i) WHEN = 00

Magnitude of Resultant:






Direction of Resultant:


i.e. the direction of resultant is in the direction of given vector (either P or Q vector)

ii) WHEN = 900

Magnitude of Resultant:



Direction of Resultant:



iii) WHEN = 1800

Magnitude of Resultant:


or,

Direction of Resultant:
The direction of the resultant is in the direction of greater vector.

Triangle Law of Vector Addition

Statement: If two vector are represented both in magnitude and direction by two sides of a triangle taken in same order than the closing side ( third side ) of triangle taken in opposite order represents theirresultant both in magnitude and direction..

Explanation:
Let two vector and are represented at both in magnitude and direction by two side and of a triangle OAC as shown in figure ii) then from trianglem law of vector addition the closing side represent their resultant .

Let be the angle between and and be the angle between and .

Magnitude of Resultant:
From C draw perpendicular, CD and OA produced.
In ODC,
OC 2 = OD 2 + CD 2
OC 2 = (OA + AD) 2 + CD 2
R 2 = (P + Q COS ) 2 + (Q Sin ) 2
On solving with R,
we get,


Direction Of Resultant:
In ODC,
=
=


eqn i) represent the magnitude of resultant and eqn ii) represent the direction of resultant with .


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