Home
Class 12
MATHS
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.`

Promotional Banner

Topper's Solved these Questions

  • Product of two Vectors

    A DAS GUPTA|Exercise Exercise|48 Videos

  • Product of three or more Vectors

    A DAS GUPTA|Exercise Exercise|28 Videos

  • Progression, Related Inequalities and Series

    A DAS GUPTA|Exercise Exercise|235 Videos

Similar Questions

Explore conceptually related problems

A line makes angles alpha,beta,gamma and delta with the diagonals of a cube.Show that cos^(2)alpha+cos^(2)beta+cos^(2)gamma+cos^(2)delta=4/3

A line makes angles alpha,beta,gamma and with the diagonals of a cube,prove that cos^(2)alpha+cos^(2)beta+cos^(2)gamma+cos^(2)delta=(4)/(3)

If a line makes angles alpha, beta, gamma, delta with the diafonals of a cubes then the value of 9(cos 2alpha + cos 2beta + cos2gamma + cos 2delta)^(2) equals ….......

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

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=

A DAS GUPTA-Product of two Vectors-Exercise
  1. The pth, qth and rth terms of a GP are the positive numbers a,b and c ...

    Text Solution

    |

  2. If vec a, vec b , vec c are mutually perpendicular vectors of equal ma...

    Text Solution

    |

  3. A line makes angles alpha,beta,gammaa n ddelta with the diagonals of a...

    Text Solution

    |

  4. vec a , vec b and vec c are the position vectors of points A ,B and C...

    Text Solution

    |

  5. Given the vectors vec A , vec B ,a n d vec C form a triangle such tha...

    Text Solution

    |

  6. If AC and BD are the diagonals of a quadrilateral ABCD, prove that its...

    Text Solution

    |

  7. A , B , Ca n dD are any four points in the space, then prove that |...

    Text Solution

    |

  8. If the angle between the vectors x vec i + vec j - vec k and vec i + x...

    Text Solution

    |

  9. If the vector vec a= x vec i + y vec j + 2 vec k is perpendicular to t...

    Text Solution

    |

  10. If vec a is a vector of magnitude 50 and parallel to vec b= 6 vec i - ...

    Text Solution

    |

  11. If vec a , vec b ,a n d vec c are unit vectors such that vec a+ vec ...

    Text Solution

    |

  12. Prove that , vec(a) xx ( vec (b) + vec(c)) + vec(b) xx (vec(c) + ...

    Text Solution

    |

  13. If vec a and vec b are vectors, each of magnitude 3 then |vec a+ vec ...

    Text Solution

    |

  14. If vecA = (1, 1, 1), vecC = (0,1,-1) are given vectors, then prove tha...

    Text Solution

    |

  15. Find a unit vector perpendicular to the plane determined by the poi...

    Text Solution

    |

  16. Let beta = 4hati + 3hatj and vec gamma be two vectors perpendicular to...

    Text Solution

    |

  17. If |vec a|=3,|vec b|=5,|vec c|=7 and vec a+vec b+vec c=0 then angle be...

    Text Solution

    |

  18. The conditions under which the vector vec P + vec Q and vec P - vec Q ...

    Text Solution

    |

  19. Let vec O A- vec a , hat O B=10 vec a+2 vec ba n d vec O C= vec b ,w ...

    Text Solution

    |

  20. Vector vec O A= hat i+2 hat j+2 hat k turns through a right angle ...

    Text Solution

    |