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Answer» If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors.The proof for the resultant vector in Parallelogram addition is as follows,Consider a parallelogram\xa0OABC\xa0as shown in the figure,Let\xa0P&Q be two adjacent sides of parallelogram, and\xa0R\xa0be the resultant vector obtained by addition of vectors\xa0P&Q.Now, drop a perpendicular from\xa0C\xa0on\xa0OA so that they meet at\xa0AFrom right angled triangle\xa0ΔOCD,OC2=OD2+DC2[OD=OA+AD]R2=(OA+AD)2+DC2R2=OA2+AD2+2OA.AD+DC2From\xa0ΔADC,\xa0AC2=AD2+DC2\xa0and also\xa0cosθ=AD/ACAnd hence\xa0R2=OA2+AD2+2OA.AD+DC2And substituting\xa0A\xa0and\xa0BR2=A2+B2+2A.Bcosθ\xa0
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