Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2015MathematicsStraight LinesActual

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, then the points ( p ₁, q ₁ ), (p₂, q₂ ) and (p₃, q₃ )

Options

  1. Aare collinear
  2. Bform an equilateral triangle
  3. Cform a sealene triangle
  4. Dform a right angled triangle

Correct answer

A. are collinear

Step-by-step solution

The equations of the lines are array l p ₁ x + q ₁ y -1=0 p ₂ x + q ₂ y -1=0 array and p ₃ x + q ₃ y -1=0 As they are concurrent, | array lll p ₁ & q ₁ & -1 p ₂ & q ₂ & -1 p ₃ & q ₃ & -1 array |=0 | array lll p ₁ & q ₁ & 1 p ₂ & q ₂ & 1 p ₃ & q ₃ & 1 array |=0 This is also the condition for the points ( p ₁, q ₁ ), ( p ₂, q ₂ ) and ( p ₃, q ₃ ) to be collinear.

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the point of intersection of the lines x=a ( 1-t^2 1+t^2 ) and y= 2 a t 1+t^2 represent (t being a parameter) 2024If the straight line 2 x+3 y-1=0, x+2 y-1=0 and a x+b y-1=0 form a triangle with origin as orthocentre, then (a, b) is equal to 2024The distance from the origin to the image of (1 , 1) with respect to the line x+y+5=0 is 2024If (-4,5) is one vertex and 7 x-y+8=0 is one diagonal of a square, then the equation of second diagonal is 2023The coordinates of the foot of the perpendicular from the point (2,3) on the line x+y-11=0 are 2023What is the angle between the two straight lines y=(2- 3 ) x+5 and y=(2+ 3 ) x-7 ? 2023If the coordinates of the points A and B be (3,3) and (7,6) , then the length of the portion of the line AB intercepted between the axes is 2023The distance between the parallel lines 3 x-4 y+7=0 and 3 x-4 y+5=0 is a b . Value of a+b is 2021 Full Straight Lines list All BITSAT PYQs