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Scalar & Vectors
Representation of vectors
Mathematical Operations
with Vectors
Scalars and Vectors (Real life example)
What is a scalar?
Scalars and Vectors (Real life example)
What is a scalar?
A scalar is a quantity that is fully described by a
magnitude only. It is described by just a number.
Examples:
Speed, volume, mass, temperature, power, energy,
time, etc.
Scalars and Vectors (Real life example)
What is a vector?
Scalars and Vectors (Real life example)
What is a vector?
Vector is a physical quantity which has magnitude
as well as direction and follows the rule of vector
addition.
Vector quantities are important in the study of
physics.
Examples:
Force, velocity, acceleration, displacement,
momentum,etc.
Scalars
and
Vectors
Scalars and Vectors (Real life example)
The marathon runner was running 20 miles per
hour towards the end zone. It is a
1
Scalar quantity
2
Vector quantity
00:15
Scalars and Vectors (Real life example)
The marathon runner was running 20 miles per
hour towards the end zone. It is a
1
Scalar quantity
2
Vector quantity
00:15
Scalars and Vectors (Real life example)
The temperature of a hall is 28 degree Celsius. It
is a
1
Scalar quantity
2
Vector quantity
00:15
Scalars and Vectors (Real life example)
The temperature of a hall is 28 degree Celsius. It
is a
1
Scalar quantity
2
Vector quantity
Solution
This is a scalar because temperature has no direction .
00:15
Scalars and Vectors (Real life example)
A bus is accelerating towards north at a rate of 3
m/s2. It is a
1
Scalar quantity
2
Vector quantity
00:15
Scalars and Vectors (Real life example)
A bus is accelerating towards north at a rate of 3
m/s2. It is a
1
Scalar quantity
2
Vector quantity
Solution
This is a vector because it represents a magnitude (3
m/s2) and a direction (towards north). This vector
represents acceleration of the bus.
00:15
Representation of vectors
Symbolic and Diagrammatic Representation
●
●
●
A vector is drawn as an arrow with a head and a tail.
The magnitude of the vector is often described by
the length of the arrow.
The arrow points in the direction of the vector.
magnitude
tail
direction
head
Symbolic and Diagrammatic Representation
How to write a vector?
Vectors are generally written with an arrow over the
top of the letter.
magnitude
Magnitude:
tail
direction
head
Types of vectors
Types of vectors
1.
2.
3.
4.
5.
Like Vectors
Equal Vectors
Opposite/Negative Vectors
Zero Vector
Unit Vector
Types of vectors
Like Vectors
-
Vectors having unequal magnitude but same
direction.
-
Ex. Velocity of 2 trains going south
Types of vectors
Equal Vectors
-
Vectors having equal magnitude and same
direction.
-
Ex. displacement covered by two trains
between Delhi and Mumbai
Types of vectors
Opposite/Negative Vectors
-
Vectors having equal magnitude but just
opposite
direction.
-
Ex. displacement covered by two trains
between Delhi and Mumbai, one going from
Mumbai to Delhi and other going from delhi
to mumbai.
Types of vectors
Zero Vectors
-
Vectors having Zero magnitude and no
significant
direction
-
Ex. velocity and displacement of a body at
rest.
Types of vectors
Unit Vectors
-
Vectors having Unit (1) magnitude and any
possible
direction
-
Ex. 1N force, 1 km displacement, 1 m/s velocity
Unit Vector (Importance)
Mathematical
Representation
of Vectors
1D vector
A vector which either lies on the coordinate axis,
or lies parallel to any of them is a 1D vector.
Ax = a i
Dx = d (- i)
By = b j
Ey = e (- j)
Cx = c k
Fx = f (- k)
2D vector
A vector which either lies on any of the coordinate
planes or parallel them.
A = Ax i + Ayj
B = Bx i + Bzk
C = Cy j + Czk
2D vector
A = Ax i + Ayj
2D vector
Resolution of a 2D vector
2D vector
Resolution of a 2D vector
2D vector
Resolution of a 2D vector
3D vector
A vector which either lies in space and not on any axis or plane.
A = Ax i + Ayj + Azk
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