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Find the angle between the diagonals of ...

Find the angle between the diagonals of a cube with edges of length "a".

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From the diagram
`overline(OG)=overline(d_(1))=alphahati+alphahatj+alphahatk,overline(CF)=overline(d_(2))=-alphahati+alphahatj+alphahatk`
`therefore` The angle angle between the diagonals is
`cos theta=(vecd_(1).vecd_(2))/(|vecd_(1)|.|vecd_(2)|)=(1)/(3)rArrtheta=cos^(-1)((1)/(3))`
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Knowledge Check

  • The angle between two diagonals of a cube İs

    A
    `cos^-1(1/3)`
    B
    `30^@`
    C
    `cos^-1(1/sqrt3)`
    D
    `45^@`

  • The angle between two diagonals of a cube will be

    A
    `sin^(-1)(1/3)`
    B
    `cos^(-1)(1/3)`
    C
    variable
    D
    none of these

  • The angle between two diagonals of a cube will be

    A
    `sin^(-1)(1/3)`
    B
    `cos^(-1)(1/3)`
    C
    variable
    D
    none of these

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