Home
Class 12
MATHS
Two systems of rectangular axes have ...

Two systems of rectangular axes have the same origin. If a plane cuts them at distance `a ,b ,c`and ` 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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos
  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a ,b ,c and a^(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 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 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))

If a, b , c are in GP, then 1/(a^(2 )−b^2 )+1/b^2 = ?

If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) 1 (c) -1 (d) 3

If the circles x^2+y^2+2a x+c=0a n dx^2+y^2+2b y+c=0 touch each other, then (a) 1/(a^2)+1/(b^2)=1/c (b) 1/(a^2)+1/(b^2)=1/(c^2) (c) a+b=2c (d) 1/a+1/b=2/c

Show that a^(2)(1+b^(2))+b^(2)(1+c^(2))+c^(2)(1+a^(2))gt abc

Simplify: -1/2a^2b^2c+1/3a b^2c-1/4a b c^2-1/5c b^2a^2+1/6c b^2a-1/7c^2a b+1/8c a^2bdot

|[1/c,1/c,-(a+b)/c^2],[-(b+c)/a^2,1/a,1/a],[(-b(b+c))/(a^2c),(a+2b+c)/(ac),(-b(a+b))/(ac^2)]| is

If (1)/(a)+(1)/(c )=(1)/(2b-a)+(1)/(2b-c) , then

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. The direction ratios of a normal to the plane through (1,0,0)a n d(...

    Text Solution

    |

  2. The centre of the circle given by vec rdot( hat i+2 hat j+2 hat k)=...

    Text Solution

    |

  3. Two systems of rectangular axes have the same origin. If a plane cu...

    Text Solution

    |

  4. Find the equation of a plane which passes through the point (3, 2, 0...

    Text Solution

    |

  5. The lines (x-2)/1=(y-3)/1=(z-4)/(-k)a n d(x-1)/k=(y-4)/2=(z-5)/1 are ...

    Text Solution

    |

  6. The point of intersection of the lines (x-5)/(3)=(y-7)/(-1)and(x+3)/(-...

    Text Solution

    |

  7. A tetrahedron has vertices of O(0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C...

    Text Solution

    |

  8. The radius of the circle in which the sphere x^(2)=y^(2)+z^(2)+2z-2y-4...

    Text Solution

    |

  9. A sphere of constant radius 2k passes through the origin and meets t...

    Text Solution

    |

  10. A plane passes through a fixed point (a,b,c). The locus of the foot of...

    Text Solution

    |

  11. Equation of the plane containing the straight line (x)/(2)= (y)/(3)= (...

    Text Solution

    |

  12. The equation of the plane through the intersection of the planes x+2y...

    Text Solution

    |

  13. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

    Text Solution

    |

  14. The vector equation of the plane passing through the origin and the ...

    Text Solution

    |

  15. The lines vec r= vec a+lambda( vec bxx vec c)a n d vec r= vec b+mu( v...

    Text Solution

    |

  16. The projection of the line (x+1)/(-1)=(y)/(2)=(z-1)/(3) on the plane x...

    Text Solution

    |

  17. The direction cosines of a line satisfy the relations lamda(l+m)=nandm...

    Text Solution

    |

  18. The intercepts made on the axes by the plane which bisects the line jo...

    Text Solution

    |

  19. The pair of lines whose direction cosines are given by the equation...

    Text Solution

    |

  20. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha,...

    Text Solution

    |