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If alpha,beta and gamma are angles made ...

If `alpha,beta and gamma` are angles made by a line with coordinate axes such that `alpha=beta=2gammaandanglealpha` is acute, then `cos alpha`=

A

`(sqrt(17)-1)/(8)`

B

`(sqrt(17)+1)/(8)`

C

`(-sqrt(17)+1)/(8)`

D

none of these

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If alpha,beta,gamma be the angles which a line makes with the coordinates axes, then

    A
    `sin^(2)alpha+sin^(2)beta+sin^(2)gamma=1`
    B
    `sin^(2)alpha+sin^(2)beta+sin^(2)gamma=1`
    C
    `cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
    D
    `cos^(2)alpha+sin^(2)beta+sin^(2)gamma=1`

  • If a line makes angles a, p and y with the coordinate axes, then cos2alpha+cos2beta+cos2gamma is

    A
    `-1`
    B
    `-2`
    C
    2
    D
    `-3`

  • If a line makes angles alpha,beta,gamma with co-ordinate axes, then cos2alpha+cos 2 beta+cos2gamma=

    A
    0
    B
    -1
    C
    2
    D
    1

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