VECTORS
Class 12 Physics — Typed & Decorated Notes
Concept • Formula • Examples
Quick-use note
These notes are rewritten in clean typed form from the uploaded handwritten pages.
Important formulas are highlighted for quick revision.
Contents
1. Scalar & Vector Quantities
2. Types of Vectors
3. Unit & Position Vectors
4. Angle Between Two Vectors
5. Resolution of a Vector
6. Triangle & Parallelogram Laws
7. Resultant Magnitude
8. Dot Product
9. Cross Product
10. Polygon Law & Worked Example
Class 12 Physics • Vectors Page 1
, 1. Scalar and Vector Quantities
Scalar Quantity
Definition
A scalar quantity has only magnitude and follows simple algebraic addition.
Examples: Mass, volume, density, time, etc.
Vector Quantity
Definition
A vector quantity has both magnitude and direction. Vector quantities follow vector laws
of addition.
Examples: Displacement, velocity, force, momentum, etc.
Scalar Vector
Only magnitude Magnitude + direction
Simple algebraic addition Vector laws of addition
2. Types of Vectors
Zero Vector
A vector having zero magnitude is called a zero vector. Its direction is not defined.
Unit Vector
A vector whose magnitude is equal to 1 is called a unit vector.
Equal Vectors
Two or more vectors having the same magnitude and the same direction are called equal
vectors.
Negative Vectors
Two vectors are negative vectors if they have the same magnitude but opposite directions.
Class 12 Physics • Vectors Page 2
Class 12 Physics — Typed & Decorated Notes
Concept • Formula • Examples
Quick-use note
These notes are rewritten in clean typed form from the uploaded handwritten pages.
Important formulas are highlighted for quick revision.
Contents
1. Scalar & Vector Quantities
2. Types of Vectors
3. Unit & Position Vectors
4. Angle Between Two Vectors
5. Resolution of a Vector
6. Triangle & Parallelogram Laws
7. Resultant Magnitude
8. Dot Product
9. Cross Product
10. Polygon Law & Worked Example
Class 12 Physics • Vectors Page 1
, 1. Scalar and Vector Quantities
Scalar Quantity
Definition
A scalar quantity has only magnitude and follows simple algebraic addition.
Examples: Mass, volume, density, time, etc.
Vector Quantity
Definition
A vector quantity has both magnitude and direction. Vector quantities follow vector laws
of addition.
Examples: Displacement, velocity, force, momentum, etc.
Scalar Vector
Only magnitude Magnitude + direction
Simple algebraic addition Vector laws of addition
2. Types of Vectors
Zero Vector
A vector having zero magnitude is called a zero vector. Its direction is not defined.
Unit Vector
A vector whose magnitude is equal to 1 is called a unit vector.
Equal Vectors
Two or more vectors having the same magnitude and the same direction are called equal
vectors.
Negative Vectors
Two vectors are negative vectors if they have the same magnitude but opposite directions.
Class 12 Physics • Vectors Page 2
