SUMMER-1 2012ADDITION OF VECTORSEXPERIMENT 3- Addition of VectorsOBJECTIVESWhen a number of forces passing through the same point, act on an object, they may be replaced by a single force which is called the resultant or the sum. The resultant therefore is a single force which is similar in effect to the effect produced by the several forces acting on the body. It is therefore a single force that replaces those forces. The objectives of this lab are to use graphical, analytic and experimental methods to:1. Resolve a force vector into its rectangular components, and2. To find the resultant of a number of forces acting on a body. APPARATUS1. Force table5. Strings for suspending the masses 2. Four weight holders6. A ring3. Four pulleys7. A metal pin4. Slotted weights8. A protractor9. A compass10. Sheets of plain or graph paper.THEORY OF VECTOR ADDITIONA.Graphical MethodsParallelogram MethodVectors are represented graphically by arrows. The length of a vector arrow (drawn to scale on graph paper) is proportional to the magnitude of the vector, and the arrow points in the direction of the vector. The length scale is arbitrary and usually selected for convenience and sothat the vector graph fits nicely on the graph paper. See Fig 1a, where R = A + B. The magnitude R of the resultant vector is proportional to the length of the diagonal arrow and the direction of the resultant vector is that of the diagonal arrow R. The direction of R may be specified as being at an angle θ relative to A.