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:
A
Promotional Banner

Topper's Solved these Questions

  • PLANE

    TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos
  • PLANE

    TARGET PUBLICATION|Exercise CRITICAL THINKING|58 Videos
  • PAIR OF STRAIGHT LINES

    TARGET PUBLICATION|Exercise EVALUATION TEST|11 Videos
  • PROBABILITY DISTRIBUTION

    TARGET PUBLICATION|Exercise Evaluation test|5 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:

TARGET PUBLICATION-PLANE-COMPETATIVE THINKING
  1. If planes x-cy-bz=0,cx-y+az=0 and bx+ay-z=0 pass through a straight li...

    Text Solution

    |

  2. IF for a plane the intercepts on the coordinate axes are 8,4,4 then th...

    Text Solution

    |

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

    Text Solution

    |

  4. The perpendicular distance of the point P(6,7,8) from xy-plane is a. 8...

    Text Solution

    |

  5. Length of the perpendicular form the point (-6,2,3) on the plane 3x-6y...

    Text Solution

    |

  6. If the distance of points 2hati+3hattj+lamdahatk from the plane r*(3ha...

    Text Solution

    |

  7. The distance between (2,1,0) and 2x+y+2z+5=0 is

    Text Solution

    |

  8. The distance of the point (1,3,-7) from the plane passing through the ...

    Text Solution

    |

  9. A plane is at a distance of 5 units form the origin and perpendicular ...

    Text Solution

    |

  10. If the length of perpendicular drawn from origin on a plane is 7 units...

    Text Solution

    |

  11. A plane passes through (1,-2,1) and is perpendicular to two planes 2x-...

    Text Solution

    |

  12. If L1 is the line of intersection of the planes 2x-2y+3x-2=0x-y+z+1=0 ...

    Text Solution

    |

  13. The equation of a plane passing through the line of intersection of th...

    Text Solution

    |

  14. The point A(-1,3,0), B(2,2,1) and C(1,1,3) determine a plane. The dist...

    Text Solution

    |

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

    Text Solution

    |

  16. In a three-dimensional x y z space , the equation x^2-5x+6=0 represent...

    Text Solution

    |

  17. The plane (x)/(a)+(y)/(b)+(z)/(c )=3 meets the co-ordinate axes in A,B...

    Text Solution

    |

  18. A plane cuts the coordinate axes X,Y,Z at A,B,C respectively such that...

    Text Solution

    |

  19. Plane ax+by+cz=1 intersect axes in A,B,C respectively. If G((1)/(6),-(...

    Text Solution

    |

  20. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |