To add the two or more than two vectors we use the polygon method in physics. Polygon method in physics is also called as polygon law of vector addition.Polygon Method in Physics:This law is use to find the resultant of two or more than two vectors.
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Polygon method in physics is the extension of triangle law of vector addition. It state that if a number of vectors can be represented by the side of the polygon in magnitude and direction taken in order, then their resultant is represented by the side which close the polygon taken in the opposite order. This resultant having both magnitude and direction.Let us find the resultant of four vectors vecA ,vecB , vecC and vecDas shown in diagram. Now we denote the vectors by bold letters.
Polygon MethodNow to find the resultant, draw the vector OK = A. Now move the vector B parallel to itself, so that the tail coincides with the tip of the vector A. Mark the tip of the vector B as L. Now, move the vector C parallel to itself, so that its tail coincides the tip of vector B and mark the tip of vector C as M. Finally, move the vector D parallel to itself, so that the tail of vector D coincides with the tip of vector C. Thus, the sides OK, KL, LM and MN taken in the same order have represented the vectors A, B, C and D.
According to the polygon law of the vector addition, the closing side ON = R taken in the opposite direction represents the sum or resultant of the vectors A, B, C and D, i.e.,A + B + C + D = RProof of Polygon Method in Physics:In triangle OKL, OK + KL = OL ….(1)In triangle OLM, OL + LM = OMPlug the value of OL by equation (1), we getOK + KL + LM = OM ….(2)In triangle OMN, OM + MN = ONPlug the value of OM by equation (2), we getOK + KL + LM + MN = ONNow, OK = A, KL = B, LM = C, MN = D and ON = RSo, A + B + C + D = R