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A line makes angles alpha,beta,gammaa n ...

A line makes angles `alpha,beta,gammaa n ddelta` with the diagonals of a cube. Show that `cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4//3.`

A

1

B

`1//3`

C

`8//3`

D

`4//3`

Text Solution

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The correct Answer is:
D
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Knowledge Check

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

    A
    `2/3`
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  • 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 =

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    `(1)/(2)`
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    `(1)/(4)`
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    `(3)/(4)`
    D
    `(4)/(3)`

  • If a line makes alpha,beta,gamma,delta angles with four diagonals of a cube, then cos2alpha+cos2beta+cos2gamma+cos2delta =

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    `-(2)/(3)`
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