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
= 0^{0}

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
= 90^{0}

Magnitude of Resultant:

Direction of Resultant:

iii) WHEN
= 180^{0}

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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