![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](https://image.slidesharecdn.com/3vectorpart1-210526120607/85/Scalars-and-Vectors-Part-1-6-320.jpg)
Scalars and Vectors Part 1
- 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.
- 3. UDAY KHANAL Department of Physics CCRC 3
- 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
- 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
- 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
- 16. Types of vector 4 Equal Vectors • Same magnitude • Same direction
- 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
- 24. Types of vector 12 Position vector 𝑟 = 𝑥𝐼 + 𝑦𝑗 + 𝑍𝑘 𝑟 = 𝑥𝐼 + 𝑦𝑗 (x , y)
- 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