Class 11 Physics: Vector Product

Introduction

• Welcome to the Class 11 Physics series.
• Current Lecture: Vector Product (Lecture Number 10)

Vector Product

• When two vectors are multiplied, the result is a vector, known as the vector product or cross product.
• The result of a cross product is a new vector.

Definition and Calculation

• Magnitude of the vector product: ( |A \times B| = |A||B|\sin(\theta) )
• ( \theta ): The angle between A and B
• Direction determination: By the right-hand thumb rule

Right-Hand Thumb Rule

• Use the right hand to rotate the fingers from A towards B.
• The direction pointed by the thumb is the direction of the vector product.

Examples and Applications

• Example: If R and F are two vectors,
  • The result of ( R \times F ) is torque.

Properties of Vector Product

• Not commutative: ( A \times B \neq B \times A )
• Distributive: ( A \times (B + C) = A \times B + A \times C )

Unit Vector

• Products of all three unit vectors:
  • ( i \times j = k )
  • ( j \times k = i )
  • ( k \times i = j )
  • ( i \times i = j \times j = k \times k = 0 )

Special Cases

• When ( \theta = 0 ) or ( 180° ), ( A \times B = 0 )
• When vectors are perpendicular, ( \theta = 90° ), ( A \times B ) is maximum.

Application

• The vector product is used in calculations of torque, angular momentum, magnetic force, etc.

Practice

• Importance of questions and exercises associated with the lecture
• Problem sheets available on the website for practice