ICTOR
Physical quantity
V
v V
Scalar quantity Tensor
quantity Vector quantity
↳ ↳ It does not have ↳These have
These have magnitude a
magnitude ,
unit and
and unit specific direction but direction.
.
,
↳ All its ↳ Vector
fundamental quantities magnitude varies
They follow the law of
are scalar with direction. addition.
↳
They are added by algebraic Examples :- ↳ The
magnitude of a vector
methods. ① Moment of inertia is always positive.
Example : - Work W, = 55
,
We -35
= ② Permittivity (E)
Then w = 5 3
- =
25 3
Permeability (M)
Representation of a vector
Symbol Graphical representation
↳ A vector
quantity is represented
capital ↳ Represented
by placing an arrow over a
by an arrow .
letter of its symbol .
-
Head
Ex : -
Force =
Tail
And
according to NCERT =
E
Bold
Magnitude =
Length of the line segment
Direction= Direction of the arrow .
F
Magnitude = = F
The vectors.
Angle between two vectors :-
angle between the directions of two
B
B
jo &
I
At
< ---
(o
>
⑮
, Y
B 0
*
Angleblw and 30 + 190-20)
=
:
T
20
=
30 + 70%
B
↓ /30 X %
100
in
=
200
200
v Angle blu Band 0 =
Angle biw and I O= 30 +90 = 120 ·
TYPE OF VECTORS
·
Parallel or codirectional vectors :
- 2 Anti-parallel vectors :-
> :
*
0 = 0 >
> 0
:
= 180
⑮
direction -
same direction-opposite
3 ↑
Equal rectors :
-
pposite or
legative vector : -
- -
> ⑮ E
magnitude and direction same
Magnitude-same , direction-opposite
= n = -
5 vectors :- 6 vector
Coplanar Null rector or zero :
Lie in the same plane Magnitude-Zero
Yx Direction-Arbitrary -
Symbol
X
- -
# + () =
I
V
>X
# Exo =
Two vectors are always
Coplanar . # A+o = 1
7 Unit vector :
Magnitude-one direction-defined ,
Three-dimensional unit vectors
Symbol -x(cap)
Vector
Yx
Unit vector =
g
- 2
Vector
Magnitude of -
"
...........
-
Units -
X
i
> X
is -
= 1 Z
-
Y
And a I =
, ① Polar vectors :-whose initial point (point of fixed.
application) is
I
-
Examples : Displacement Force etc.
I ,
P :
Fixed point
9 Axial vectors-their direction is along the quis of rotation.
"W
Examples : Angular velocity
Torque , 9)
momentum etc.
Angular ↑
point If a vector is displaced in free space without changing its direction,
it remains unchanged.
ms of vector addition
T
1
right-order · [ ·
pposite-order
I
Triangle law : -If two vectors acting simultaneously on a particle are represented in
magnitude and direction by two sides of a triangle taken in order ,
then
Their resultant is represented in magnitude and direction by the third side
of the
triangle taken in the opposite order.
*
⑰
# D
&
B B
&
D
⑰
-
R =+ 5 -
D
~
'R = + m -
2
From equation ① and ②
* =+ Vector addition is commutative .
Physical quantity
V
v V
Scalar quantity Tensor
quantity Vector quantity
↳ ↳ It does not have ↳These have
These have magnitude a
magnitude ,
unit and
and unit specific direction but direction.
.
,
↳ All its ↳ Vector
fundamental quantities magnitude varies
They follow the law of
are scalar with direction. addition.
↳
They are added by algebraic Examples :- ↳ The
magnitude of a vector
methods. ① Moment of inertia is always positive.
Example : - Work W, = 55
,
We -35
= ② Permittivity (E)
Then w = 5 3
- =
25 3
Permeability (M)
Representation of a vector
Symbol Graphical representation
↳ A vector
quantity is represented
capital ↳ Represented
by placing an arrow over a
by an arrow .
letter of its symbol .
-
Head
Ex : -
Force =
Tail
And
according to NCERT =
E
Bold
Magnitude =
Length of the line segment
Direction= Direction of the arrow .
F
Magnitude = = F
The vectors.
Angle between two vectors :-
angle between the directions of two
B
B
jo &
I
At
< ---
(o
>
⑮
, Y
B 0
*
Angleblw and 30 + 190-20)
=
:
T
20
=
30 + 70%
B
↓ /30 X %
100
in
=
200
200
v Angle blu Band 0 =
Angle biw and I O= 30 +90 = 120 ·
TYPE OF VECTORS
·
Parallel or codirectional vectors :
- 2 Anti-parallel vectors :-
> :
*
0 = 0 >
> 0
:
= 180
⑮
direction -
same direction-opposite
3 ↑
Equal rectors :
-
pposite or
legative vector : -
- -
> ⑮ E
magnitude and direction same
Magnitude-same , direction-opposite
= n = -
5 vectors :- 6 vector
Coplanar Null rector or zero :
Lie in the same plane Magnitude-Zero
Yx Direction-Arbitrary -
Symbol
X
- -
# + () =
I
V
>X
# Exo =
Two vectors are always
Coplanar . # A+o = 1
7 Unit vector :
Magnitude-one direction-defined ,
Three-dimensional unit vectors
Symbol -x(cap)
Vector
Yx
Unit vector =
g
- 2
Vector
Magnitude of -
"
...........
-
Units -
X
i
> X
is -
= 1 Z
-
Y
And a I =
, ① Polar vectors :-whose initial point (point of fixed.
application) is
I
-
Examples : Displacement Force etc.
I ,
P :
Fixed point
9 Axial vectors-their direction is along the quis of rotation.
"W
Examples : Angular velocity
Torque , 9)
momentum etc.
Angular ↑
point If a vector is displaced in free space without changing its direction,
it remains unchanged.
ms of vector addition
T
1
right-order · [ ·
pposite-order
I
Triangle law : -If two vectors acting simultaneously on a particle are represented in
magnitude and direction by two sides of a triangle taken in order ,
then
Their resultant is represented in magnitude and direction by the third side
of the
triangle taken in the opposite order.
*
⑰
# D
&
B B
&
D
⑰
-
R =+ 5 -
D
~
'R = + m -
2
From equation ① and ②
* =+ Vector addition is commutative .
