Home
Class 12
MATHS
A line makes acute angles of alpha,beta ...

A line makes acute angles of `alpha,beta and gamma` with the coordinate axes such that `cosalpha,cosbeta=cosbeta,cosgamma=2/9 and cosgamma cosalpha=4/9` then `cosalpha+cosbea+cosgamma` is equal to

A

`(25)/9`

B

`5/9`

C

`5/3`

D

`2/3`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `cosalphacosbeta=cosbetacosgamma=2/9 and cosgammacosalpha=4/9`
`therefore" "cosalpha=2/3,cosbeta=1/3 and cosgamma=2/3`
`rArr" "cosalpha+cosbeta+cosgamma=2/3+1/3+2/3=5/3`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

  • THREE DIMENSIONAL GEOMETRY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

  • STRAIGHT LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2(MISCELLANEOUS PROBLEMS)|30 Videos

  • TRIGONOMETRIC FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|26 Videos

Similar Questions

Explore conceptually related problems

If a line makes angles alpha,beta and gamma with the coordinate axes,then prove that cos2 alpha+cos2 beta+cos2 gamma=-1

If a line makes angle alpha, beta and gamma with the coordinate axes respectively, then cos2alpha+cos 2 beta+cos 2gamma=

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

A line makes angles alpha,beta and gamma with the coordinate axes.If alpha+beta=90^(@), then find gamma

If a line makes angles alpha, beta, gamma with the coordinate axes, prove that sin^2alpha+sin^2beta+sin^2gamma=2

If a line makes angle "alpha","beta\ and\ gamma" with the coordinate axes, find the value of "cos"2"alpha"+"cos"2"beta"+"cos"2"gamma"dot

If a line makes the angles alpha,beta,gamma with the axes, then what is the value of 1+cos2alpha+cos2beta+cosgamma equal to

If cosalpha,cosbeta,cosgamma are the direction cosines of a vector veca , then cos2alpha+cos2beta+cos2gamma is equal to

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-THREE DIMENSIONAL GEOMETRY-Exercise 2 (MISCELLANEOUS PROBLEMS)
  1. If OA is equally inclined to OX,OY ,OZ and if A is sqrt(3) units from ...

    Text Solution

    |

  2. If P(0,1,2),Q(4,-2,1) and O(0,0,0) are three points, then /POQ=

    Text Solution

    |

  3. A line makes the same angle theta with each of the x and z-axes. If t...

    Text Solution

    |

  4. If the directions cosines of a vector of magnitude 3 are (2/3,(-a)/3,2...

    Text Solution

    |

  5. If 1/2,1/3,n are direction cosines of a line, then the value of n is

    Text Solution

    |

  6. A line makes an angle theta both with x-axis and y-axis. A possible ra...

    Text Solution

    |

  7. The direction cosines to two lines at right angles are (1,2,3) and (-2...

    Text Solution

    |

  8. A line makes acute angles of alpha,beta and gamma with the coordinate ...

    Text Solution

    |

  9. The direction rations of the diagonals of a cube which joins the origi...

    Text Solution

    |

  10. The projection of the line segment joining (2,5,6) and (3,2,7) on the ...

    Text Solution

    |

  11. In DeltaABC the mid points of the sides AB, BC and CA are (l, 0, 0),...

    Text Solution

    |

  12. The diection cosines of two lines are proportional to (2,3,-6) and (3,...

    Text Solution

    |

  13. The angle between the lines whose direction cosines are (sqrt3/4,1/4,s...

    Text Solution

    |

  14. Let O be the origin and P be the point at a distance 3 units from orig...

    Text Solution

    |

  15. If the points A(2,3,-4), B(1,-2,3) and C(3,lambda,-1) are colliner, th...

    Text Solution

    |

  16. If the directions cosines of a straight line are ltk,k,kgt then

    Text Solution

    |

  17. Find the angle between the following pair of lines: A lines with direc...

    Text Solution

    |

  18. If P(p), Q(q), R(r) and S(s) be four points such that 3p+8q=6r+5s then...

    Text Solution

    |

  19. The direction cosines of line joining (1,-1,1) and (-1,1,1) are

    Text Solution

    |

  20. A vector r is inclined at equal angles to OX,OY and OZ If the magnitud...

    Text Solution

    |