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  • IF vector a ,vector b ,vector c and vector d are unit vectors such that (vector a cross vector b) dot (vector c cross vector d )=1 and vector a dot vector c =1/2 then

IF vector a ,vector b ,vector c and vector d are unit vectors such that (vector a cross vector b) dot (vector c cross vector d )=1 and vector a dot vector c =1/2 then

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Solution:   Let   heta _1, be the angle between  veca and vecb,

                  heta_2   be the angle between  vecc and vecd

              and  phi be the angle between  veca imes vecb and vecc imes vecd

          Then ,

          

    Rightarrow      (veca imes vecb)cdot (vecc imes vecd)=1  Possible only when   

              left | veca imesvecb ight |=left | vecc imesvecd ight |=1    and   (veca imesvecb)parallel (vecc imesvecd)

 Since    vecacdot vecc=frac12    and    vecbparallel vecd,  then  left | vecc imes vecd ight | eq 1. 

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Deependra Verma

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