Home
Class 12
MATHS
Two system of rectangular axes have the ...

Two system of rectangular axes have the same origin. If a plane cuts them at distance `a, b, c and a', b', c'` from the origin, then:

A

`(1)/(a^(2))+(1)/(b^(2))-(1)/(c^(2))+(1)/(a'^(2))+(1)/(b'^(2))-(1)/(c'^(2))=0`

B

`(1)/(a^(2))-(1)/(b^(2))-(1)/(c^(2))+(1)/(a'^(2))-(1)/(b'^(2))-(1)/(c'^(2))=0`

C

`(1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))+(1)/(a'^(2))-(1)/(b'^(2))-(1)/(c'^(2))=0`

D

`(1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))+(1)/(a'^(2))+(1)/(b'^(2))+(1)/(c'^(2))=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (LEVEL 2( SINGLE CORRECT ANSWER TYPE QUESTIONS))|30 Videos
  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS)|23 Videos
  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (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

Two system of rectangular axes have the same origin. IF a plane cuts them at distances a,b,c and a\',b\',c\' from the origin then (A) 1/a^2+1/b^2-1/c^2+1/a^(\'2)+1/b\^(\'2)-1/c^(\'2)=0 (B) 1/a^2-1/b^2-1/c^2+1/a^(\'2)-1/b\^(\'2)-1/c^(\'2)=0 (C) 1/a^2+1/b^2+1/c^2-1/a^(\'2)-1/b\^(\'2)-1/c^(\'2)=0 (D) 1/a^2+1/b^2\+1/c^2+1/a^(\'2)+1/b\^(\'2)+1/c^(\'2)=0

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a ,b ,cand a^prime ,b^(prime),c ' from the origin, then a. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0 b. 1/(a^2)-1/(b^2)-1/(c^2)+1/(a^('2))-1/(b^('2))-1/(c^('2))=0 c. 1/(a^2)+1/(b^2)+1/(c^2)-1/(a^('2))-1/(b^('2))-1/(c^('2))=0 d. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a ,b ,ca n da^(prime),b^(prime),c^(prime) respectively, prove that 1/(a^2)+1/(b^2)+1/(c^2)=1/(a^('2))+1/(b^('2))+1/(c^('2))

Two system of rectangular axes have the same origin. If the plane cuts the axes at dostances a, b, c to the first system and a', b', c' to the second system of rectangular axes from the origin then

If the perpendicular distance of a point A other than the origin from the plane x+y+z=p is equal to the distance of the plane from the origin,then the coordinates of p are (A) (p,2p,0)(B)(0,2p,-p)(C)(2p,p,-p)(D)(2p,-p,2p)

If the perpendicular distance of point A other than origin from the plane x+y+z=k is equal to the distance of the plane from the origin ,then A -=

A circle of radius r passes through the origin O and cuts the axes at A and B . Let P be the foot of the perpendicular from the origin to the line AB . Find the equation of the locus of P .

If (x,y) and (X,Y) be the coordinates of the same point referred to two sets of rectangular axes with the same origin and if ax+by becomes pX+qY, where a,b are independent of x,y, then

The distance of the B(6,6) from the origin is:

MCGROW HILL PUBLICATION-THE DIMENSIONAL GEOMETRY -SOLVED EXAMPLES (LEVEL 1( SINGLE CORRECT ANSWER TYPE QUESTIONS))
  1. A plane which passes through the point (3,2,0) nd the line (x-4)/1=(y-...

    Text Solution

    |

  2. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

    Text Solution

    |

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

    Text Solution

    |

  4. The two lines x=ay+b, z=cy+d and x= a' y+ b', z= c' y +d' will be perp...

    Text Solution

    |

  5. Distance between two parallel planes 2x+y+2z=8 and 4x+2y+4z+5=0 is

    Text Solution

    |

  6. A tetrahedron has vertices P(1,2,1),Q(2,1,3),R(-1,1,2) and O(0,0,0). T...

    Text Solution

    |

  7. A line line makes the same angle theta with each of the x and z-axes....

    Text Solution

    |

  8. A line with direction cosines proportional to 2,1,2 meet each of the l...

    Text Solution

    |

  9. If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=...

    Text Solution

    |

  10. The angle between the lines 2x=3y=-z and 6x=-y=-4z is (A) 0^0 (B) 90^0...

    Text Solution

    |

  11. If the angle theta between the line (x+1)/(1)=(y-1)/(2)=(z-2)/(2) and ...

    Text Solution

    |

  12. The distance between the line vecr = 2i - 2j + 3k + lamda(i - j + 4k)...

    Text Solution

    |

  13. then image of the point (-1,3,4) in the plane x-2y=0

    Text Solution

    |

  14. Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=...

    Text Solution

    |

  15. If a line makes an angle of pi/4 with the positive directions of ea...

    Text Solution

    |

  16. Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(...

    Text Solution

    |

  17. If the angle between the line x=(y-1)/(2)=(z-3)(lambda) and the plane ...

    Text Solution

    |

  18. The distance of the point (1,-5,9) from the plane x-y+z=5 measured alo...

    Text Solution

    |

  19. The length of the perpendicular drawn from the point (3, -1, 11) to th...

    Text Solution

    |

  20. An equation of a plane parallel to the plane x-2y +2 z-5=0 and at a un...

    Text Solution

    |