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P.T the smaller angle theta between any ...

P.T the smaller angle `theta` between any two diagonals of a cube is given by `cos theta = 1//3`

Text Solution

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The correct Answer is:
`=(1)/(3)`
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The angle between any two diagonals of a cube is

Prove that th angle theta between any two diagonals of a cube is given by costheta=(1)/(3) .

Knowledge Check

  • Angle between the diagonal of a cube and diagonal of a face of the cube is

    A
    `sin^(-1)((1)/(3))`
    B
    `cos^(-1)((1)/(3))`
    C
    `cos^(-1)(sqrt((2)/(3)))`
    D
    `cos^(-1)((2)/(3))`

  • In a unit cube. Find The angle between a diagonal of a cube and the diagonal of a face of the cube

    A
    `Cos^(-1)(1//sqrt3)`
    B
    `Cos^(-1)(1//3)`
    C
    `Cos^(-1)(2//3)`
    D
    `Cos^(-1)(sqrt(2//3))`

  • If the angle 2 theta is acute then the acute angle between the pair of straight lines x^(2) (cos theta - sin theta) + 2xy cos theta + y^(2) (cos theta + sin theta) = 0 is

    A
    `2 theta`
    B
    `(theta)/(2)`
    C
    `(theta)/(3)`
    D
    `theta`

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