If the lines p₁x + q₁y = 1, p₂x + q₂y = 1 and p₃x + q₃y = 1 be concurrent, then the points (p₁, q₁), (p₂, q₂) and (p₃, q₃)

Correct Answer is : are collinear

Correct Answer is : are collinear

Test Index

BITSAT 2015 Paper

Section: Mathematics

Question : 117 of 150

Marks: +1, -0

If the lines

p_1x

q_1y

p_2x

q_2y

p_3x + q_3y

(p_1, q_1)

(p_2, q_2)

(p_3, q_3)

Solution:

The equations of the lines are

p_1x + q_1y

-1 = 0 ...(i)

p_2x + q_2y

-1 = 0 ...(ii)

and

p_3x + q_3y

-1 = 0 ...(iii)

As they are concurrent,

\begin{vmatrix} p_1 & q_1 & -1 \\ p_2 & q_2 & -1 \\ p_3 & q_3 & -1 \end{vmatrix}

= 0

⇒

\begin{vmatrix} p_1 & q_1 & 1 \\ p_2 & q_2 & 1 \\ p_3 & q_3 & 1 \end{vmatrix}

= 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

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