Home
Class 12
MATHS
The direction cosines of the lines bisec...

The direction cosines of the lines bisecting the angle between the line whose direction cosines are `l_1, m_1, n_1 and l_2, m_2, n_2` and the angle between these lines is `theta`, are

A

`(l_1+l_2)/(2sin((theta)/(2))), (m_1+m_2)/(2sin((theta)/(2))), (n_1+n_2)/(2sin((theta)/(2)))`

B

`(l_1+l_2)/(2cos((theta)/(2))), (m_1+m_2)/(2cos((theta)/(2))), (n_1+n_2)/(2cos((theta)/(2)))`

C

`(l_1-l_2)/(2sin((theta)/(2))), (m_1-m_2)/(2sin((theta)/(2))), (n_1-n_2)/(2sin((theta)/(2)))`

D

`(l_1-l_2)/(2cos((theta)/(2))), (m_1-m_2)/(2cos((theta)/(2))), (n_1-n_2)/(2cos((theta)/(2)))`

Text Solution

Verified by Experts

The correct Answer is:
(b)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 4|7 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

The direction cosines of the lines bisecting the angle between the lines whose direction cosines are l_(1),m_(1),n_(1) and l_(2),m_(2),n_(2) and the angle between these lines is theta, are

The direction cosines of the lines bisecting the angle between the lines whose direction cosines are I_(1),m_(1),n_(1) and I_(2),m_(2),n_(2) and the angle between these lines is theta ,are

Find the angle between the lines whose direction-cosines are give /+2m+3n=0 and 3/m-4/n+mn=0'

The angle between the lines whose direction cosines are proportional to (1,2,1) and (2,-3,6) is

Two lines with direction cosines l_(1),m_(1),n_(1) and l_(2), m_(2), n_(2) are at right angle of

The direction cosines of a line bisecting the angle between two perpendicular lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (1)(l_1+l_2)/2,(m_1+m_2)/2,(n_1+n_2)/2 (2)l_1+l_2,m_1+m_2,n_1+n_2 (3)(l_1+l_2)/(sqrt(2)),(m_1-m_2)/2,(n_1+n_2)/(sqrt(2)) (4)l_1-l_2,m_1-m_2,n_1-n_2 (5)"n o n eo ft h e s e"

Find the angle between the line whose direction cosines are given by l+m+n=0 and 2l^(2)+2m^(2)-n^(2)-0

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to 1,-1,2 and 2,1,-1 are

The angle between the lines whose directionn cosines are given by 2l-m+2n=0, lm+mn+nl=0 is

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. A line passes through the point (6, -7, -1) and (2, -3, 1). The direct...

    Text Solution

    |

  2. If P is a point in space such that OP is inclined to OX at 45^(@) and ...

    Text Solution

    |

  3. The direction cosines of the lines bisecting the angle between the lin...

    Text Solution

    |

  4. The equation of the plane perpendicular to the line (x-1)/(1), (y-2)/(...

    Text Solution

    |

  5. The locus of a point which moves so that the difference of the squares...

    Text Solution

    |

  6. The position vectors of points a and b are hat(i)-hat(j)+3hat(k) and 3...

    Text Solution

    |

  7. The vector equation of the plane through the point 2hat(i)-hat(j)-4hat...

    Text Solution

    |

  8. Let L1 be the line r1=2hat(i)+hat(j)-hat(k)+lambda(hat(i)+2hat(k)) and...

    Text Solution

    |

  9. For the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3), which one of the following...

    Text Solution

    |

  10. The value of m for which straight line 3x-2y+z+3=0=4x-3y+4z+1 is paral...

    Text Solution

    |

  11. The length of projection of the line segmet joining the points (1, 0,...

    Text Solution

    |

  12. The number of planes that are equidistant from four non-coplanar po...

    Text Solution

    |

  13. In a three dimensional co-odinate , P, Q and R are images of a point A...

    Text Solution

    |

  14. A plane passing through (1,1,1) cuts positive direction of coordinates...

    Text Solution

    |

  15. If lines x=y=za n dx=y/2=z/3 and third line passing through (1,1,1) fo...

    Text Solution

    |

  16. The point of intersecting of the line passing through (0, 0, 1) and in...

    Text Solution

    |

  17. Two system of rectangular axes have the same origin. If a plane cuts t...

    Text Solution

    |

  18. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

    Text Solution

    |

  19. Consider the following 3lines in space L1:r=3hat(i)-hat(j)+hat(k)+la...

    Text Solution

    |

  20. Let r=a+lambdal and r=b+mum br be two lines in space, where a= 5hat(i)...

    Text Solution

    |