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Given that (vecbeta-vecalpha).(vecbeta+v...

Given that `(vecbeta-vecalpha).(vecbeta+vecalpha)=8` and `vecalpha.vecbeta=2` Also `|vec alpha|=1` then angle between `(vecbeta-vecalpha)` and `(vecbeta+vecalpha)` is

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A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, vecb=vecalpha+3vecbeta . If |vecalpha|=|vecbeta|=2 and angle between vecalpha and vecbeta is pi/3 then the length of a diagonal of the parallelogram is (A) 4sqrt(5) (B) 4sqrt(3) (C) 4sqrt(7) (D) none of these

A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, vecb=vecalpha+3vecbeta. If |vecalpha|=|vecbeta|=2 and angle between vecalpha and vecbeta is pi/3 then the length of a diagonal of the parallelogram is (A) 4sqrt(5) (B) 4sqrt(3) (C) 4sqrt(7) (D) none of these

A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, vecb=vecalpha+3vecbeta. If |vecalpha|=|vecbeta|=2 and angle between vecalpha and vecbeta is pi/3 then the length of a diagonal of the parallelogram is

A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, vecb=vecalpha+3vecbeta. If |vecalpha|=|vecbeta|=2 and angle between vecalpha and vecbeta is pi/3 then the length of a diagonal of the parallelogram is

Prove that vec R+([ vec Rdot( vecbetaxx( vecbetaxx vecalpha))] vecalpha)/(| vecalphaxx vecbeta|^2)+([ vec Rdot( vecalphaxx( vecalphaxx vecbeta))] vecbeta)/(| vecalphaxx vecbeta|^2)=([ vec R vecalpha vecbeta]( vecalphaxx vecbeta))/(| vecalphaxx vecbeta|^2)

Prove that vec R+([ vec Rdot( vecbetaxx( vecbetaxx vecalpha))] vecalpha)/(| vecalphaxx vecbeta|^2)+([ vec Rdot( vecalphaxx( vecalphaxx vecbeta))] vecbeta)/(| vecalphaxx vecbeta|^2)=([ vec R vecalpha vecbeta]( vecalphaxx vecbeta))/(| vecalphaxx vecbeta|^2)

Prove that vec R+([ vec Rdot( vecbetaxx( vecbetaxx vecalpha))] vecalpha)/(| vecalphaxx vecbeta|^2)+([ vec Rdot( vecalphaxx( vecalphaxx vecbeta))] vecbeta)/(| vecalphaxx vecbeta|^2)=([ vec R vecalpha vecbeta]( vecalphaxx vecbeta))/(| vecalphaxx vecbeta|^2)

Prove that vec R+([ vec Rdot( vecbetaxx( vecbetaxx vecalpha))] vecalpha)/(| vecalphaxx vecbeta|^2) +([ vec Rdot( vecalphaxx( vecalphaxx vecbeta))] vecbeta)/(| vecalphaxx vecbeta|^2) =([ vec R vecalpha vecbeta]( vecalphaxx vecbeta))/(| vecalphaxx vecbeta|^2)