If a vector + b vector + c vector= 0 then prove that a*b=b*c=c*a

Question

Aman Kashyap · Answer

vectorA + vectorB + vectorC =0vectorA*(vectorA +vectorB + vectorC)=vectorA*0(vectorA*vectorA) + (vectorA*vectorB) + (vectorA*vectorC) =00 + vectorA*vectorB - vectorCvectorA =0vectorA*vectorB = vectorC*vectorA..........(1)AgainvectorA + vectorB + vectorC = 0vectorB*(vectorA + vectorB + vectorC = 0*vectorBvectorB*vectorA + vectorB*vectorB + vector C*vectorB = 0-vectorA*vectorB + 0 + vectorC*vectorB =0vectorC*vectorB = vectorA*vectorB......(2)From (1) and (2) we havevectorA*vectorB = vectorB*vectorC = vectorC*vectorAHence Proved.

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If a vector + b vector + c vector= 0 then prove that ab=bc=c*a

If a vector + b vector + c vector= 0 then prove that ab=bc=c*a

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If a vector + b vector + c vector= 0 then prove that a*b=b*c=c*a

If a vector + b vector + c vector= 0 then prove that a*b=b*c=c*a

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If a vector + b vector + c vector= 0 then prove that ab=bc=c*a

If a vector + b vector + c vector= 0 then prove that ab=bc=c*a