Home
Class 12
MATHS
A=[{:(l(1),m(1),n(1)),(l(2),m(2),n(2)),(...

`A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}]` and `B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}]`
Where `p_(i), q_(i),r_(i)` are the co-factors of the elements `l_(i), m_(i), n_(i)` for `i=1,2,3`. If `(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2))` and `(l_(3),m_(3),n_(3))` are the direction cosines of three mutually perpendicular lines then `(p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2))` and `(p_(3),q_(),r_(3))` are

A

the direction cosines of three mutually perpendicular lines

B

the direction ratios of three mutually perpendicular lines which are not direction cosines

C

the direction cosines of three lines which need be perpendicular

D

the direction ratios but not the direction cosines of three lines which need not be perpendicular

Text Solution

Verified by Experts

The correct Answer is:
(a)
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

If l_(1), m_(1), n_(1), l_(2), m_(2), n_(2) and l_(3), m_(3), n_(3) are direction cosines of three mutuallyy perpendicular lines then, the value of |(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3))| is

Let l_(i),m_(i),n_(i);i=1,2,3 be the direction cosines of three mutually perpendicular vectors in space.Show that AA=I_(3) where A=[[l_(2),m_(2),n_(2)l_(3),m_(3),n_(3)]]

The direction cosines of a line equally inclined to three mutually perpendiclar lines having direction cosines as l_(1),m_(1),n_(1),l_(2),m_(2),n_(2) and l_(3), m_(3),n_(3) are

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 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.

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_(i)^(2)+m_(i)^(2)+n_(i)^(2)=1 , (i=1,2,3) and l_(i)l_(j)+m_(i)m_(j)+n_(i)n_(j)=0,(i ne j,i,j=1,2,3) and Delta=|{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}| then

If three mutually perpendicular lines have direction cosines (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) and (L_(3),m_(3),n_(3)) then the line having direction cosines l_(1)+l_(2)+l_(3),m_(1)+m_(2)+m_(3), and n_(1)+n_(2)+n_(3) ,make an angle of

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. Show that x(1) hati+y(1) hatj+ z1hatk, x2hati+y2hatj+z2hatk and x3hati...

    Text Solution

    |

  2. The position vectors of points of intersection of three planes rcdotn1...

    Text Solution

    |

  3. A pentagon is formed by cutting a triangular corner from a rectangular...

    Text Solution

    |

  4. In a dimensional coodinate a system P, Q and R are image of a point A(...

    Text Solution

    |

  5. A plane 2x+3y+5z=1 has a point P which is at minimum distance from lin...

    Text Solution

    |

  6. The locus of point which moves in such a way that its distance from th...

    Text Solution

    |

  7. A cube C={(x, y, z)|o le x, y, zle1} is cut by a sharp knife along the...

    Text Solution

    |

  8. A ray of light is sent through the point P(1, 2, 3,) and is reflected ...

    Text Solution

    |

  9. A plane cutting the axes in P, Q, R passes through (alpha-beta, beta-g...

    Text Solution

    |

  10. The shortest distance between any two opposite edges of the tetrahedro...

    Text Solution

    |

  11. The angle between the pair of planes represented by equation 2x^2-2y^2...

    Text Solution

    |

  12. Let (p, q, r) be a point on the plane 2x+2y+z=6, then the least value ...

    Text Solution

    |

  13. The fout lines drawing from the vertices of any tetrahedron to the cen...

    Text Solution

    |

  14. The shorteast distance from (1, 1, 1) to the line of intersection of t...

    Text Solution

    |

  15. The shortest distance between the two lines L1:x=k1, y=k2 and L2: x=k3...

    Text Solution

    |

  16. A=[{:(l(1),m(1),n(1)),(l(2),m(2),n(2)),(l(3),m(3),n(3)):}] and B=[{:(p...

    Text Solution

    |

  17. If ABCD is a tetrahedron such that each triangleABC, triangleABD and t...

    Text Solution

    |

  18. In a regular tetrahedron, if the distance between the mid points of op...

    Text Solution

    |

  19. A variable plane makes intercepts on X, Y and Z-axes and it makes a t...

    Text Solution

    |

  20. If P, Q, R, S are four coplanar points on the sides AB, BC, CD, DA of ...

    Text Solution

    |