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Find the point of intersection of the th...

Find the point of intersection of the three planes `vecr.veca=1, vecr.vecb=1,vecr.vecc=1` where `veca,vecb,vecc` are three non_coplaner vector.

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Solve veca.vecr=x, vecb.vecr=y, vecc.vecr=z , where veca,vecb,vecc are given non coplanar vectors.

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Knowledge Check

  • If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non-coplanar, then

    A
    `vecrbot(veccxxveca)`
    B
    `vecrbot(vecaxxvecb)`
    C
    `vecrbot(vecbxxvecc)`
    D
    `vecr=vec0`

  • The vector equation of the line of intersection of the planes vecr=vecb+lamda_1 (vecb-veca) + mu_1 (veca-vecc) and vecr=vecc+lamda_2(vecb-vecc)+mu_2(veca+vecb) veca,vecb,vecc being non - coplanar vectors, is

    A
    `vecr = vecb+mu_1 (veca+vecc)`
    B
    `vecr = vecb+lamda_1 (veca-vecc)`
    C
    `vecr = 2vecb+lamda_2 (veca-vecc)`
    D
    None of these

  • Statement 1: Any vector in space can be uniquely written as the linear combination of three non-coplanar vectors. Stetement 2: If veca, vecb, vecc are three non-coplanar vectors and vecr is any vector in space then [(veca,vecb, vecc)]vecc+[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb=[(veca, vecb, vecc)]vecr

    A
    1
    B
    2
    C
    3
    D
    4

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    Explore conceptually related problems

    Assertion: If vecr.veca=0, vecr.vecb=0, vecr.vecc=0 for some non zero vector vecr e then veca,vecb,vecc are coplanar vectors. Reason : If veca,vecb,vecc are coplanar then veca+vecb+vecc=0 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

    If vecr.veca=vecr.vecb=vecr.vecc=0 for some non-zero vectro vecr , then the value of [(veca, vecb, vecc)] is

    If vecP = (vecbxxvecc)/([vecavecbvecc]).vecq=(veccxxveca)/([veca vecb vecc])and vecr = (vecaxxvecb)/([veca vecbvecc]), " where " veca,vecb and vecc are three non- coplanar vectors then the value of the expression (veca + vecb + vecc ). (vecq+ vecq+vecr) is

    Let vecr be a non - zero vector satisfying vecr.veca = vecr.vecb =vecr.vecc =0 for given non- zero vectors veca vecb and vecc Statement 1: [ veca - vecb vecb - vecc vecc- veca] =0 Statement 2: [veca vecb vecc] =0

    If vecp=(vecbxxvecc)/([(veca,vecb,vecc)]),vecq=(veccxxveca)/([(veca,vecb,vecc)]),vecr=(vecaxxvecb)/([(veca,vecb,vecb)]) where veca,vecb,vecc are three non-coplanar vectors, then the value of the expression (veca+vecb+vecc).(vecp+vecq+vecr) is

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