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

If `veca, vecb and vecc` are vectors such that `veca, vecb = veca, vecc, veca xx vecb = veca xx vecc, a ne 0.` then show that `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, and vecc are unit vectors such that veca +2vecb +2vecc =vec0 , then |veca xx vecc| is equal to :

    A
    `(1)/(4)`
    B
    `(sqrt(15))/(16)`
    C
    `(15)/(16)`
    D
    `(sqrt(15))/(4)`

  • If veca,vecb, vecc are three vectors such that veca + vecb +vecc =vec0, |veca| =1 |vecb| =2, | vecc| =3 , then veca.vecb + vecb .vecc +vecc + vecc.veca is equal to

    A
    1
    B
    0
    C
    -7
    D
    7

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    Explore conceptually related problems

    given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca is not a zero vector. Show that vecb=vecc .

    given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca is not a zero vector. Show that vecb=vecc .

    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=0 , then show that veca xx vecb = vecb xx vecc = vecc xx veca .

    If veca, vecb and vecc are three non zero vectors such that veca xx vecb = vecc and vecbxx vecc = veca. Prove that veca, vecb and vecc are mutually at right angles and |vecb|=1 and |vecc| =|veca|

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