This document provides tips for taking online classes and guidelines for participating in online class sessions. It recommends being prepared before class starts, treating the online course seriously, being accountable, managing your time well, having a dedicated study space, eliminating distractions, figuring out how you learn best, actively participating, and leveraging your network. During class sessions, it advises opening your camera, muting your audio when not speaking, having necessary materials ready, not writing on the shared screen, asking permission before sharing, and being disciplined.
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Watch this slide to learn:
1) Types of quantities?
2) Representation of matrix in Euclidean space?
3) Vector ( in terms of matrix )?
4) Unit vector
5) Operations on vector in MATLAB:
6) Parametric equation of line
7) Cross product
8) Vector dot product
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1. TIPS FOR TAKING ONLINE CLASS
FOR YOURSELF
1: Be ready before the starting time
2: Treat an online course like a real course
3: Hold yourself accountable
4: Practice time management
5: Create a regular study space and stay organized
6: Eliminate distractions
7: Figure out how you learn best
8: Actively participate
9: Leverage your network
INSIDE THE CLASS
1: Open your camera
2: Mute your audio
3: take your pen, copy and other material sources
3: Don’t add your note on the screen
4: Do ask, write and share after the permission. It
will be provided at the end of the class
5: Be more disciplined.
1
2. This is a REGULAR CLASS. Please make a
note by writing down what you have
seen here.
Make a separate note for CURRENT
ELECTRICITY.
5. Scalars
Definition: Those
physical quantities
having magnitude
only.
Obeying vector algebra
Vectors
Definition: Those physical quantities having magnitude
and fixed direction as well as obeying vector algebra.
Magnitude and
direction
Not obeying vector algebra
Tensors
Definition: Those physical
quantities having magnitude
direction but not obeying
vector algebra.
Magnitude
only
Physical
Quantities
Direction is not
important
Direction is not a
vector direction
Ex: mass, length
Ex: velocity, acceleration
Ex: current, pressure
6. Remember:
The physical quantity having magnitude and direction is not necessarily a vector.
The addition condition is that it must obey vector algebra [ to be discussed later] ex:
current, pressure, time
7. Geometrical representation of
a Vector
Directed line segment
A B
Initial Final
Tail Head
Here the directed line
segment AB with
arrow head
represents a vector.
Notation : 𝐴𝐵 or AB or P (say) or 𝑃
Magnitude : |𝐴𝐵| or AB or P (say) or |𝑃|
Arrow head is always
from left to right
Arrow head
8. Graphical Representation of a Vector
Suppose a car is moving
with a velocity of 25 m/s in
a direction of 45 degree
north east. It is graphically
represented as;
Graphically a vector can be represented by a directed line segment with an arrow head drawn
to a fixed magnitude.
Illustration:
E
N
- - - - - - - - - - - - - - - - - - - - - - - - - Reference line
𝟒𝟓°
o
Head
Tail
Remember : Arrow head is
always from initial to final.
𝑷
V Scale : 5 mm = 1 m/s
H Scale : 5 mm = 1 m/s
9.
10. Note: A vector can be shifted parallelly from one point to another keeping
its magnitude and direction same
11. Angle between two Vectors
Tail -Tail coincide Head -Head coincide Head -Tail coincide
- - - - - -
𝜃
𝜃
𝜃
Internal Internal External
T
T
T
H
H
H
12. 1 Null Vector * Vector having zero magnitude
Note: Head and tail coincide
Ex: • Velocity of stationary object
• Origin of coordinate
• Acceleration of object moving with constant velocity
If, 𝐴- 𝐵 = 0
Null vector
Types of vector
13. 2 Unit Vector * Vector having Unit magnitude
Unit vector of 𝐴 is 𝐴 (A – cap or hat).
It can be written as,
𝐴 = A 𝐴
Magnitude Direction
Unit vector gives the
direction.
𝐴 =
𝐴
𝐴
Types of vector
14.
15. Types of vector
The unit vectors along the direction of
X – axis is 𝑖,
Y – axis is 𝑗, and
Z – axis is 𝑘 are called orthogonal unit vectors.
∴ 𝑋 = 𝑋𝑖
𝑌 = 𝑌𝑗
𝑍 = 𝑍𝑘
3 Orthogonal Unit Vectors
17. Types of vector
5 Negative Vectors • Same magnitude
• Opposite direction
18. Types of vector
6 Collinear Vectors • Vectors acting along the common
support whatever be their
magnitude
Same line
19. Types of vector
7 Parallel Vectors • Same direction
• Magnitude of one vector is scalar
multiple of another
All the four vectors shown in the image below are parallel
to each other because all of them can be expressed as a
scalar multiple of each other.
Scalar multiple
20. Types of vector
8 Anti Parallel Vectors • Opposite direction
• Magnitude of one vector is scalar
multiple of another
Scalar multiple
𝐴
𝐵 = - 2 𝐴
21. Types of vector
9 Coplanar Vectors • Vectors lying on the same plane
22. Types of vector
10 Orthogonal Vectors • Vectors perpendicular to each other
90°
𝐴
𝐵
23. Types of vector
11 Coinitial Vectors • Vectors having same initial point
𝐴 𝐵
𝐶
𝑂
25. Types of vector
13 Displacement vector
P(x1,y1)
Q(x2,y2)
∆𝑟 = 𝑟2 − 𝑟1
𝑟2
𝑟1
Initial
Final
O
26. Types of vector
14 Polar vector • Vector having straight line effect
Ex: Force
27. Types of vector
15 Pseudo Vectors (Axial) • The st. line effect of polar vectors give
rise to another vector called pseudo or
axial vectors.
Ex: rotational effect of force – Torque
rotational effect of linear momentum – angular momentum
