JEE & NEET Revision Notes
Comprehensive Digital Version for System Compatibility
1. Vector Algebra (Detailed)
Vector Representation: &vec;A = |&vec;A| Â
• Â (Unit Vector) is used to specify direction.
• Unit Vector Formula: Â = &vec;A / |&vec;A|.
• Note: It is dimensionless and has a magnitude of 1.
Resultant of Two Vectors (R)
Formula: R = √(A² + B² + 2AB cosθ)
Special Cases:
• Parallel Vectors (θ = 0°): R = A + B (Maximum Resultant)
• Anti-parallel (θ = 180°): R = A - B (Minimum Resultant)
• Perpendicular (θ = 90°): R = √(A² + B²)
• Equal Magnitude (A = B): R = 2A cos(θ/2)
Direction (α): tan α = (B sin θ) / (A + B cos θ)
Types of Vectors & Laws
• Subtraction: &vec;S = &vec;A + (-&vec;B) = √(A² + B² - 2AB cosθ)
• Polygon Law: Applicable for addition of multiple vectors.
2. Trigonometry & Quadrants
Important values for Physics problems (Mechanics, Forces):
Angle (θ) sin θ cos θ tan θ
37° 3/5 (0.6) 4/5 (0.8) 3/4 (0.75)
Comprehensive Digital Version for System Compatibility
1. Vector Algebra (Detailed)
Vector Representation: &vec;A = |&vec;A| Â
• Â (Unit Vector) is used to specify direction.
• Unit Vector Formula: Â = &vec;A / |&vec;A|.
• Note: It is dimensionless and has a magnitude of 1.
Resultant of Two Vectors (R)
Formula: R = √(A² + B² + 2AB cosθ)
Special Cases:
• Parallel Vectors (θ = 0°): R = A + B (Maximum Resultant)
• Anti-parallel (θ = 180°): R = A - B (Minimum Resultant)
• Perpendicular (θ = 90°): R = √(A² + B²)
• Equal Magnitude (A = B): R = 2A cos(θ/2)
Direction (α): tan α = (B sin θ) / (A + B cos θ)
Types of Vectors & Laws
• Subtraction: &vec;S = &vec;A + (-&vec;B) = √(A² + B² - 2AB cosθ)
• Polygon Law: Applicable for addition of multiple vectors.
2. Trigonometry & Quadrants
Important values for Physics problems (Mechanics, Forces):
Angle (θ) sin θ cos θ tan θ
37° 3/5 (0.6) 4/5 (0.8) 3/4 (0.75)
