# Learn How to Calculate Resultant Vector using Parallelogram Law of Forces - Tutorial

## How to Calculate Resultant Vector using Parallelogram Law of Forces - Definition, Formula, Example

##### Definition:

Parallelogram is a schematic figure with two set of similar sides. Parallelogram Law of Forces states that if any two given forces acting at a point are indicated in magnitude and direction by the two contiguous sides of a parallelogram, then their outcome is signified in magnitude and direction by the diagonal passing through the point, where magnitude specifies the vectors size or quantity and direction specifies how the vector is directed from one location to another.

##### Formula: ###### Where,

R = Magnitude of resultant vector α = Direction of resultant vector P = Magnitude of vector P Q = Magnitude of vector Q θ = Angle between two vectors

##### Example :

Consider that in a parallelogram, the magnitude of a vector P as 3N, another magnitude of vector Q as 4N and angle between two vectors is 30 degrees. Calculate the resultant force vector using parallelogram law of forces

##### Given,

Magnitude of vector [P] = 3N, Magnitude of vector [Q] = 4N, Angle = 30 degrees

##### To find,

Resultant force vector using parallelogram law of forces

###### Step 1:

Substitute the value of P and Q in the formula,

R = √32 + 42 + (2 x 3 x 4 x cos(30)) R = √9 + 16 + 20.7846 R = 6.77N

###### Step 2:

Let us now calculate the value of α. tan α = (4 x sin 30) / ( 3 + 4 cos 30) tan α = 4 x 0.5 / (3 + ( 4 x 0.866)) tan α = 0.309405941 α = tan -1(0.309405941) α = 17.2o