Home
Class 11
MATHS
If the lines p1x+q1y=1+q2y=1 and p3x+q3y...

If the lines `p_1x+q_1y=1+q_2y=1 and p_3x+q_3y=1` be concurrent, show that the point `(p_1,q_1),(p_2,q_2) and (p_3,q_3)` are collinear.

Text Solution

Verified by Experts

The correct Answer is:
`p_(1)q_(2)-p_(2)q_(1)+p_(2)q_(3)-p_(3)q_(2)+p_(3)q_(1)-p_(1)q_(3)=0`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    MODERN PUBLICATION|Exercise Exercise 10.1|14 Videos

  • STRAIGHT LINES

    MODERN PUBLICATION|Exercise Exercise 10.2|20 Videos

  • STRAIGHT LINES

    MODERN PUBLICATION|Exercise OBJECTIVE TYPE QUESTIONS (C . True/False questions)|5 Videos

  • STATISTICS

    MODERN PUBLICATION|Exercise Chapter Test|7 Videos

  • TRIGONOMETRY

    MODERN PUBLICATION|Exercise Chapter Test (3)|12 Videos

Similar Questions

Explore conceptually related problems

If the lines p_1x+q_1y=1,p_2x+q_2y=1a n dp_3x+q_3y=1, be concurrent, show that the point (p_1, q_1),(p_2, q_2)a n d(p_3, q_3) are collinear.

If the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.

If the lines p_(1)x+q_(1)y=1+q_(2)y=1 and p_(3)x+q_(3)y=1 be concurrent,show that the point (p_(1),q_(1)),(p_(2),q_(2)) and (p_(3),q_(3)) are collinear.

If veca,vecb be two non zero non parallel vectors then show that the points whose position vectors are p_1veca+q_1vecb,p_2veca+q_2vecb,p_3veca+q_3vecb are collinear if |(1,p_1,q_1),(1,p_2,q_2),(1,p_3,q_3)|=0

the lines (p+2q)x+(p-3q)y=p-q for different values of p&q passes trough the fixed point is:

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

MODERN PUBLICATION-STRAIGHT LINES -OBJECTIVE TYPE QUESTIONS (D . Very short answer type questions)
  1. Find the equation of the bisectors of the angles between the coordinat...

    Text Solution

    |

  2. Find the equation of the line passing through the point (2, 2) and inc...

    Text Solution

    |

  3. Find the length of intercepts cuts on axes from the line x sin alpha+y...

    Text Solution

    |

  4. Find the tangent of the angle between the lines whose intercepts on th...

    Text Solution

    |

  5. If 3x-by+2=0 and 9x+3y+a=0 represent the same straight line, find the ...

    Text Solution

    |

  6. Find the point of intersection of the line, x/3 - y/4 = 0 and x/2 + y/...

    Text Solution

    |

  7. The length of the perpendicular form the point (b,a) to the line x/a-y...

    Text Solution

    |

  8. Which of the st.lines 2x-y+3=0 and x-4y-7=0 is farther from the origin...

    Text Solution

    |

  9. Find the transformed equation of the curve y^(2)-4x+4y+8=0 when the or...

    Text Solution

    |

  10. Find the equation of the straight lines passing through the origin mak...

    Text Solution

    |

  11. What acute angle does a line of slope -(2)/(3) make with a vertical li...

    Text Solution

    |

  12. Find the angle between the st. Lines : (a+b)x+(a-b)y=2ab and (a-b)x+...

    Text Solution

    |

  13. State whether the st.lines : x-y-1=0, 4x+3y=25 and 2x-3y+1=0 are con...

    Text Solution

    |

  14. Statement 1 : The chord of contact of the circle x^2+y^2=1 w.r.t. the ...

    Text Solution

    |

  15. Find the equation of the linepassing through the point (sqrt(2, 2 sqrt...

    Text Solution

    |

  16. Find the equation of the line for which (i)p=3 and alpha=45^(@) (ii...

    Text Solution

    |

  17. Reduce the equation x+2y=3 to the intercept form.

    Text Solution

    |

  18. Find the equation of a line parallel to the line 3x-4y+2=0 and passing...

    Text Solution

    |

  19. If the lines p1x+q1y=1+q2y=1 and p3x+q3y=1 be concurrent, show that th...

    Text Solution

    |

  20. Two sides of a square lie on the lines x+y=1a n dx+y+2=0. What is its ...

    Text Solution

    |