Home
Class 12
MATHS
If l(1), m(1), n(1) and l(2),m(2),n(2) a...

If `l_(1), m_(1), n_(1)` and `l_(2),m_(2),n_(2)` are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are `m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1)`.

A

`l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2)=0`

B

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

C

`(l_(1))/(l_(2))+(m_(1))/(m_(2))+(n_(1))/(n_(2))=1`

D

`(l_(1))/(l_(2))+(m_(1))/(m_(2))+(n_(1))/(n_(2))=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise EXERCISE (LEVEL 2 (SINGLE CORRECT ANSWER TYPE QUESTIONS))|16 Videos

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise EXERCISE (NUMERICAL ANSWER TYPE QUESTIONS)|20 Videos

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise EXERCISE (CONCEPT-BASED (SINGLE CORRECT ANSWER TYPE QUESTIONS ))|15 Videos

  • STATISTICS

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|13 Videos

  • TRIGONOMETRICAL IDENTITIES AND EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

If l_1,""""m_1,""""n_1 and l_2,""""m_2,""""n_2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m_1n_2-m_2n_1, n_1l_2-n_2l_1, l_1m_2-l_2m_1 .

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 "l"_1,("\ m")_1,("\ n")_1("\ and\ l")_2,("\ m")_2,"n"_2 be the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of them are ("m"_1("\ n")_2-"m"_2"n"_1),"\ "("n"_1"l"_2-"n"_2"l"_1),"\ "("l"_1"m"_2-"l"_2"m"_1)dot

Let l_(1),m_(1),n_(1);l_(2),m_(2),n_(2) and l_(3),m_(3),n_(3) be the direction cosines of three mutually perpendicular lines.Show that the direction ratios of the line which makes equal angles with each of them are (l_(1)+l_(2)+l_(3)),(m_(1)+m_(2)+m_(3)),(n_(1)+n_(2)+n_(3))

If l_(1),m_(1),n_(2);l_(2),m_(2),n_(2), be the direction cosines of two concurrent lines,then direction cosines of the line bisecting the angles between them are proportional to

If l_(1),m_(1),n_(1) and l_(2),m_(2),n_(2) are the directional cosines of two vectors and theta is the angle between them, then their value of cos theta is

l = m = n = 1 are the direction Cosines of

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.

MCGROW HILL PUBLICATION-THE DIMENSIONAL GEOMETRY -EXERCISE (LEVEL 1 (SINGLE CORRECT ANSWER TYPE QUESTIONS))
  1. The coordinate of the foot of the perpendicular from the point (a,b,c)...

    Text Solution

    |

  2. l = m = n = 1 are the direction Cosines of

    Text Solution

    |

  3. If l(1), m(1), n(1) and l(2),m(2),n(2) are the direction cosines of tw...

    Text Solution

    |

  4. A(0,5,6),B(1,4,7),C(2,3,7) dnD(3,4,6) are four points in space. The po...

    Text Solution

    |

  5. P(1,1,1) and Q(lamda,lamda,lamda) are two points in space such that PQ...

    Text Solution

    |

  6. Show that the points (0,7,10), (-1,6,6) and(-4,9,6) are the vertices o...

    Text Solution

    |

  7. If alpha, beta, gamma are the angles which a line makes with the coord...

    Text Solution

    |

  8. If a line makes angles alpha,beta,gamma with the positive direction of...

    Text Solution

    |

  9. Find the vector equation of the line through A(3,4,-7)a n dB(1,-1,6)do...

    Text Solution

    |

  10. The lines (x-1)/3=(y-1)/(-1)=(z+1)/0 and (x-4)/2=(y+0)/0=(z+1)/3 (A) i...

    Text Solution

    |

  11. The sine of the angle between the lines r=2i+2j-k+(i+j+k)t and the pla...

    Text Solution

    |

  12. Equation of a plane passing through (1, 1, 1) and containing x-axis is

    Text Solution

    |

  13. The co-ordinates of the foot of the perpendicular from the point (3,-1...

    Text Solution

    |

  14. The length of the line segment whose projection on the coordinate axes...

    Text Solution

    |

  15. The number of lines which are equally inclined to the axes is :

    Text Solution

    |

  16. Find the equation of a line which passes through a given point of posi...

    Text Solution

    |

  17. If the line r=(i+j-k)+lambda(3i-j)andr=(4i-k)+mu(2i+3k) intersect at t...

    Text Solution

    |

  18. Line of intersection of the two planes barr.(3i - j + k)=1 and barr.(i...

    Text Solution

    |

  19. The plane x-2y+7z+21=0 (A) contains the line (x+1)/(-3)=(y-3)/2=(z+2)/...

    Text Solution

    |

  20. A line passes through two points A(2,-3,-1) and B(8,-1,2). The coordin...

    Text Solution

    |