Home
Class 12
MATHS
If the direction cosines of two lines ar...

If the direction cosines of two lines are `l_(1), m_(1), n_(1)` and `l_(2), m_(2), n_(2)`, then find the direction cosine of a line perpendicular to these lines.

A

`l_(1)+l_(2),m_(1)+m_(2),n_(1)+n_(2)`

B

`l_(1)-l_(2),m_(1)-m_(2),n_(1)-n_(2)`

C

`m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1)`

D

`l_(1)+2l_(2),m_(1)+2m_(2),n_(1)+2n_(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    TARGET PUBLICATION|Exercise Competitive Thinking|37 Videos

  • THREE DIMENSIONAL GEOMETRY

    TARGET PUBLICATION|Exercise Evaluation Test|9 Videos

  • THREE DIMENSIONAL GEOMETRY

    TARGET PUBLICATION|Exercise Evaluation Test|9 Videos

  • PROBABILITY DISTRIBUTION

    TARGET PUBLICATION|Exercise Evaluation test|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise Evaluation Test|34 Videos

Similar Questions

Explore conceptually related problems

The direction Cosines of two lines at right angles are l_(1),m_(1),n_(1)and l_(2),m_(2),n_(2) Then the direction cosines of a line which is perpendicular to both these lines are

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

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two lines and l , m, n are the direction cosines of a line perpendicular to the given two lines, then

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) The angle between the lines whose direction cosines are (1/2, 1/2,1/sqrt(2)) and (-1/2, -1/2, 1/sqrt(2)) is

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If l_(1)=1/sqrt(3), m_(1)=1/sqrt(3) then the value of n_(1) is equal to

If theta is the angle between two lines whose d.c's are (l_(1),m_(1),n_(1)) and (l_(2),m_(2),n_(2)) then the lines are perpendicular if and only if

The direction cosines to two lines at right angles are (1,2,3) and (-2,1/2,1/3) then the direction cosine prependicular to both the given lines are

If l,m,n are direction cosines of the line then -l,-m,-n can be

If (l,m,n) are direction cosines of a line then L^(2)+m^(2)+n^(2)

TARGET PUBLICATION-THREE DIMENSIONAL GEOMETRY -Critical Thinking
  1. A line passes through the point (6, -7, -1) and (2, -3, 1). The direct...

    Text Solution

    |

  2. If first two numbers of the direction cosines of a line joining points...

    Text Solution

    |

  3. If the points (2,a,-1),(3,4,b)and(1,-2,3) are collinear, the values of...

    Text Solution

    |

  4. If (1,a,1),(3,-1,2)and(1,a^(2),1) are collinear, then the values of a ...

    Text Solution

    |

  5. Points (-2, 4, 7), (3, -6 -8) and (1, -2, -2) are

    Text Solution

    |

  6. If the angle between the lines whose direction cosines are a,(-2)/(3),...

    Text Solution

    |

  7. The acute angle between the lines having direction ratios 5,4,1 and -3...

    Text Solution

    |

  8. Find the angle between the lines whose direction ratios are: 2,-3,4 ...

    Text Solution

    |

  9. Let theta be the angle between the lines AB and AC, where A, B and C a...

    Text Solution

    |

  10. The direction cosines l, m and n of two lines are connected by the rel...

    Text Solution

    |

  11. Find the angle between the line whose direction cosines are given ...

    Text Solution

    |

  12. The direction cosines of a line equally inclined to three mutually per...

    Text Solution

    |

  13. Find the angle between any two diagonals of a cube.

    Text Solution

    |

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

    Text Solution

    |

  15. If the line joining the points (-2,1,-8) and (a, b, c) is parallel to ...

    Text Solution

    |

  16. If A,B,C,D are (2,3,-1),(3,5,-3),(1,2,3),(3,5,7) respectively, then th...

    Text Solution

    |

  17. Direction ratios of two lines are a ,b ,ca n d1//b c ,1//c a ,1//a ...

    Text Solution

    |

  18. If the direction cosines of two lines are l(1), m(1), n(1) and l(2), m...

    Text Solution

    |

  19. The direction cosines of a line perpendicular to lines whose direction...

    Text Solution

    |

  20. Find the direction cosines of the line which is perpendicular to the l...

    Text Solution

    |