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Determine the values of alpha ,beta , ga...

Determine the values of `alpha ,beta , gamma ` when `[{:( 0, 2beta, gamma),( alpha ,beta, -gamma),( alpha ,-beta, gamma):}]` is orthogonal.

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Determine the values of alpha, beta, gamma when [{:(0,2sinbeta,tan gamma),(cos alpha, sin beta,-tan gamma),(cos alpha, -sin beta, tan gamma):}] is orthogonal.

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Knowledge Check

  • If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

    A
    0
    B
    1
    C
    8
    D
    2

  • If alpha, beta and gamma are the roots of the equation px^(3)+qx^(2)+r=0 , then the value of the determinant |(alphabeta, beta gamma,gamma alpha),(beta gamma, gamma alpha, alphabeta),(gamma alpha, alpha beta,beta gamma)| is

    A
    pq
    B
    qr
    C
    0
    D
    pr

  • If alpha,beta,gamma are the roots of x^(3)+ax^(2)+b=0 , then the value of |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| is equal to

    A
    `-a^(3)`
    B
    `a^(3)-ab`
    C
    `a^(3)`
    D
    `a^(2)-3b`

    • Similar Questions

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    If [(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] is orthogonal, then find the value of 2alpha^(2)+6beta^(2)+3gamma^(2).

    If alpha,beta,gamma are the roots of px^(2)+qx^(2)+r=0 then the value of the determinant det[[alpha beta,beta gamma,gamma alphabeta gamma,gamma alpha,alpha betagamma alpha,alpha beta,beta gamma]] is p b.q c.0 d.r

    If alpha,beta,gamma,in(0,(pi)/(2)), then prove that (si(alpha+beta+gamma))/(sin alpha+sin beta+sin gamma)<1

    cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta) =

    sin (beta+ gamma- alpha) + sin (gamma+ alpha - beta) + sin (alpha + beta- gamma)- sin (alpha + beta + gamma)=

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