The document explains the parallelogram law of forces, which defines the relationship between the sides and diagonals of a parallelogram and provides a method for vector addition. It includes mathematical expressions related to the law and outlines special cases based on the angle between the forces. For more detail, it provides a link to additional resources.

1. Parallelogram Law of
Forces
An introduction

2. What is Parallelogram Law?
An identity stating relation between sides and diagonals of a
parallelogram.
(𝑨𝑩) 𝟐+(𝑩𝑪) 𝟐+(𝑪𝑫) 𝟐+(𝑨𝑫) 𝟐= (𝑨𝑪) 𝟐+(𝑩𝑫) 𝟐
Sum of the squares of sides of
parallelogram is equal to the sum of
squares of diagonals of parallelogram.

3. Parallelogram Law of Vector
Addition
Modification of Parallelogram Law to facilitate addition of
vector quantities.
𝑨 2
+ 𝑩 2
+ 2 × 𝑨 × 𝑩 cos 𝜃 = 𝑸𝑺 2
𝑨 + 𝑩 = 𝑸𝑺
𝜽

4. Parallelogram Law of Forces
Application of Parallelogram Law of Vector Addition.
𝐹1
2
+ 𝐹2
2
+ 2 × 𝐹1 × 𝐹2 cos 𝜃 = 𝑸𝑺 2
𝑭 𝟏 + 𝑭 𝟐 = 𝑭

5. Special Cases
Case 1
• 𝜃 = 0°
• cos 𝜃 = 1
• sin 𝜃 = 0
• 𝑭 = 𝑭 𝟏 + 𝑭 𝟐
• 𝜶 = 𝟎°
Case 2
• 𝜃 = 180°
• cos 𝜃 = −1
• sin 𝜃 = 0
• 𝑭 = (𝑭 𝟏 ± 𝑭 𝟐) 𝟐
• 𝜶 = 𝟎° 𝒐𝒓 𝟏𝟖𝟎°
Case 3
• 𝜃 = 90°
• cos 𝜃 = 0
• sin 𝜃 = 1
• 𝑭 = 𝑭 𝟏
𝟐
+ 𝑭 𝟐
𝟐
• 𝜶 = 𝐭𝐚𝐧−𝟏(
𝑭 𝟐
𝑭 𝟏
)

6. Hey Friend,
This was just a summary on Parallelogram Law Force. For more
detailed information on this topic, please type the link given below or
copy it from the description of this PPT and open it in a new browser
window.
www.transtutors.com/homework-help/civil-
engineering/fundamental-concepts/parallelogram-law-
force.aspx