If two forces acting at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant isrepresented in magnitude and direction by the diagonal passing through the point.

*Parallelogram law of forces*

*If two forces acting at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant isrepresented in magnitude and direction by the diagonal passing through the point.*

**Explanation**

*Consider two forces Vector P and Vector Q acting at a point O inclined at an angle θ as shown in Fig..*

*The forces Vector P and Vector Q are represented in magnitude and direction by the sides OA and OB of a parallelogram OACB as shown in Fig.*

*The resultant Vector R of the forces Vector P and Vector Q is the diagonal OC of the parallelogram. The magnitude of the resultant is*

*R = root[ P2 +Q2 + 2PQcos* *θ ]*

*The direction of the resultant is α = tan-1[ Qsin θ / P+Qcos θ ]*

*Triangle law of forces*

*The resultant of two forces acting at a point can also be found by using triangle law of forces.*

*If two forces acting at a point are represented in magnitude and direction by the two adjacent sides of a triangle taken in order, then the closing side of the triangle taken in the reversed order represents the resultant of the forces in magnitude **and direction.*

*Forces Vector P and Vector Q act at an angle θ. In order to find the resultant of **Vector P and Vector Q, one can apply the head to tail method, to construct **the triangle.*

*In Fig., OA and AB represent Vector P and Vector Q in magnitude and **direction. The closing side OB of the triangle taken in the reversed order represents the resultant Vector R of the forces Vector P and Vector Q. The magnitude and the direction of Vector R can be found by using sine and cosine laws of triangles.*

*The triangle law of forces can also be stated as, if a body is in equilibrium under the action of three forces acting at a point, then the three forces can be completely represented by the three sides of a triangle taken in order.*

*If Vector P , Vector Q and Vector R are the three forces acting at a point and they **are represented by the three sides of a triangle then P/QA =Q/AB =R/ OB.*

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Parallelogram and Triangle law of forces |

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