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If veca, vecb, vecc are vectors such tha...

If `veca, vecb, vecc` are vectors such that `|vecb|=|vecc|` then `{(veca+vecb)xx(veca+vecc)}xx(vecbxxvecc).(vecb+vecc)=`

Answer

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If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

Knowledge Check

  • If veca, vecb, vecc are vectors such that veca.vecb=0 and veca + vecb = vecc then:

    A
    `|veca|^(2) + |vecb|^(2) = |vecc|^(2)`
    B
    `|veca|^(2) = |vecb|^(2) + |vecc|^(2)`
    C
    `|vecb|^(2) = |veca|^(2) + |vecc|^(2)`
    D
    None of these

  • If veca, vecb, vecc are unit vectors such that veca. vecb=0, (veca-vecc).(vecb+vecc)=0 and vecc=lambdaveca+muvecb+omega(veca xx vecb) , where lambda, mu, omega are scalars, then

    A
    `mu^(2)+omega^(2)=1`
    B
    `lambda+mu=1`
    C
    `(mu+1)^(2)+mu^(2)+omega^(2)=1`
    D
    `lambda^(2)+mu^(2)=1`

  • If veca, vecb, vecc are any three non coplanar vectors, then (veca+vecb+vecc).(vecb+vecc)xx(vecc+veca)

    A
    `0`
    B
    `[(veca, vecb, vecc)]`
    C
    `2[(veca, vecb, vecc)]`
    D
    `3[(veca, vecb, vecc)]`

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    If the vectors veca, vecb, and vecc are coplanar show that |(veca,vecb,vecc),(veca.veca, veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|=0

    If veca, vecb, vecc and vecd ar distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecc-vecb)ne 0, i.e., veca.vecb + vecd.vecc nevecd.vecb + veca.vecc.

    If veca,vecb,vecc are coplanar vectors , then show that |{:(veca,vecb,vecc),(veca*veca,veca*vecb,veca*vecc),(vecb*veca,vecb*vecb,vecb*vecc):}|=vec0

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