state parallelogram law of vector addition. derive analytically expression for magnitude and direction of resultant vector 

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when 2 vectors are represented as adjescent side of a parallelogram , the diagonal indicate the resultant  vector

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let boac be the parallelogram , ob -vector b and oa - vector a

extend a tod and join c to d

boa =theta and coa = alpha

oc be the diagonal  ie , resultant vector -r

then, in ocd

oc2 = od2 +cd2

ie, r2 = (oa+ad)2 +cd2

  = oa2+2oa *ad +ad2 + cd2  (a+b)2

in acd, ad2+cd2= ac2  - ( 1)


in acd, cos theta = ad / ac

 ad=ac cos theta 

vectorb cos theta

ac= vector b ,  ab = ac

  (1) =  vec a2 + 2abcostheta+b2

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  • Parallelogram law of vector addition

If tow vectors are acting  simultaneouslyy at a point which are represented in magnitued and direction by the tow adujustance side of a parallelogram , then the diagonal of the parallelogram passing through the point  represents the resultant and the direction 

I hope this help u must......

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