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If alpha,beta ,gamma are direction angle...

If `alpha,beta ,gamma` are direction angles of a line , then `cos 2alpha , cos 2beta + cos 2 gamma = `

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If alpha, beta , gamma are direction-angles of a line, prove that (i) cos2alpha + cos 2 beta +cos2 gamma+ 1 = 0 . (ii) cos 2 alpha + cos 2 beta + cos 2 gamma = -1 .

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Knowledge Check

  • If alpha,beta, gamma are the direction angles of a vector and cos alpha=(14)/(15), cos beta=(1)/(3) , then cos gamma=

    A
    `pm(2)/(15)`
    B
    `pm(1)/(5)`
    C
    `pm (1)/(15)`
    D
    `pm (4)/(15)`

  • If a line makes angles alpha,beta,gaama with axes of coordinates then cos 2 alpha + cos 2 beta+ cos 2 gamma=

    A
    -2
    B
    -1
    C
    1
    D
    2

  • A line makes angles alpha, beta, gamma, delta with the diagonals of a cube, then cos^(2) alpha + cos^(2)beta + cos^(2)gamma + cos^(2)delta =

    A
    `(1)/(2)`
    B
    `(1)/(4)`
    C
    `(3)/(4)`
    D
    `(4)/(3)`

    • Similar Questions

    Explore conceptually related problems

    Statement 1: If cos alpha,cos beta, and cos gamma are the direction cosines of any line segment,then cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1. Statement 2: If cos alpha,cos beta,and cos gamma are the direction cosines of any line segment,then cos2 alpha+cos2 beta+cos2 gamma=1

    If (l,m,n) are the direction cosines of a line then cos^(2)alpha+cos^(2)beta+cos^(2)gamma=

    " If "(l,m,n)" are directional cosines of a line,then "cos^(2)alpha+cos^(2)beta+cos^(2)gamma=

    If alpha,beta,gamma are acute angle such that cos alpha=tan beta,cos beta=tan gamma and cos gamma=tan alpha then

    If a line makes angles alpha, beta, gamma with the coordinate axes, prove that cos2alpha + cos 2beta + cos2gamma + 1 = 0 .

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