Home
Class 12
MATHS
If the quadrilateral formed by the line...

If the quadrilateral formed by the lines `ax+by+cz=0, ax+b'y+c=0, a'x+by+c'=0, a'x+b'y+c'=0` have perpendicular diagonals, then :

A

`b^(2)+c^(2)=b'^(2)+c'^(2)`

B

`c^(2)+a^(2)=c'^(2)+a'^(2)`

C

`a^(2)+b^(2)=a'^(2)+b'^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CARTESIAN SYSTEM OF RECTANGULAR CO-ORDINATES AND STRAIGHT LINES

    MODERN PUBLICATION|Exercise Latest Questions from AIEEE/JEE Examinations|12 Videos

  • CARTESIAN SYSTEM OF RECTANGULAR CO-ORDINATES AND STRAIGHT LINES

    MODERN PUBLICATION|Exercise Recent Competitive Questions (Questions from Karnataka CET & COMED)|8 Videos

  • CARTESIAN SYSTEM OF RECTANGULAR CO-ORDINATES AND STRAIGHT LINES

    MODERN PUBLICATION|Exercise Recent Competitive Questions (Questions from Karnataka CET & COMED)|8 Videos

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise RCQ.s Recent Competitive Questions (Questions from Karnataka CET & Comed|6 Videos

  • CIRCLES AND SYSTEMS OF CIRCLES

    MODERN PUBLICATION|Exercise Recent Competitive Questions (RCQs)|12 Videos

Similar Questions

Explore conceptually related problems

If the quadrilateral formed by the lines a x+b y+c=0, a^(prime) x+b^(prime) y+c=0 a x+b y+c^(prime)=0, a^(prime) x+b^(prime) y+c^(prime)=0 have perpendicular diagonals, then

Area of the rhombus bounded by the four lines, ax +- by +-c = 0 is

The distance between the parallel planes: ax + by + cz + d = 0 and ax + by+ cz + d' =0 is :

The three lines a x+b y+c=0, b x+c y+a=0 and c x+a y+b=0 are concurrent only when

Find the centroid of the triangle formed by the line 2x + 3y - 6 = 0, with the coordinate axes.

The value of a for which the lines represented by ax^(2)+5xy +2y^(2) = 0 are mutually perpendicular is

Equation of the plane passing through the line of intersection of the planes P= ax + by + cz + d = 0, P^(') = a^(')x + b^(')y + c^(')z + d^(') = 0 and parallel to x-axis it

If the line ax+by+c=0 is a normal to the curve xy=1 , then :

Find dy/dx if ax+by+c=0

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant is equidistant from the two axes, then :

MODERN PUBLICATION-CARTESIAN SYSTEM OF RECTANGULAR CO-ORDINATES AND STRAIGHT LINES -Multiple Choice Questions (LEVEL-II)
  1. If x(1), x(2), x(3) as well as y(1), y(2), y(3) are in G.P. with the s...

    Text Solution

    |

  2. Let PQR be a right-angled isosceles triangle right-angled at P(2, 1). ...

    Text Solution

    |

  3. If the quadrilateral formed by the lines ax+by+cz=0, ax+b'y+c=0, a'x+...

    Text Solution

    |

  4. If two vertices of a triangle are (5, -1) and (-2, 3) and if orthocent...

    Text Solution

    |

  5. If the points (1, 2) and (3, 4) were to be on the same side of the lin...

    Text Solution

    |

  6. A straight rod of length 9 units slides with its ends A, B always on t...

    Text Solution

    |

  7. The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance...

    Text Solution

    |

  8. A (1, 3) and C(7, 5) are two opposite vertices of a square. The equati...

    Text Solution

    |

  9. The diagonals of a parallelogram PQRS are along the line x+3y=4 and 6x...

    Text Solution

    |

  10. Let n be the number of points having rational co-ordinates equidistant...

    Text Solution

    |

  11. If the vertices of an equilateral triangle have rational co-ordinates...

    Text Solution

    |

  12. If the lines y=m(r )x, r=1, 2, 3 cut off equal intercepts on the trans...

    Text Solution

    |

  13. If a=(tan theta)/(tan 3theta), then the point P(a, a^(2)) :

    Text Solution

    |

  14. If two sides of a triangle are represented by : 2x-3y+4=0 and 3x+2y-...

    Text Solution

    |

  15. The distance of the point (1, 2) from the line x+y=0 measured parallel...

    Text Solution

    |

  16. If a, b, c are the pth, qth and rth terms of an H.P., then the lines b...

    Text Solution

    |

  17. If alpha beta gt 0, ab gt 0 and the variable line (x)/(a), (y)/(b)=1 i...

    Text Solution

    |

  18. A ray of light coming from the point (1, 2) is reflected at a point A ...

    Text Solution

    |

  19. If two vertices of an equilateral triangle have integral co-ordinates,...

    Text Solution

    |

  20. Let A(1, 2) and B(3, 4) be two points. Let C(x, y) be a point such th...

    Text Solution

    |