Question -
Answer -
Given:
m1x – y + c1 =0 … (1)
m2x – y + c2 =0 … (2)
m3x – y + c3 =0 … (3)
It is given that thethree lines are concurrent.
Now, consider thefollowing determinant:
m1(-c3 +c2) + 1(m2c3-m3c2) + c1(-m2 +m3) = 0
m1(c2-c3)+ m2(c3-c1) + m3(c1-c2)= 0
∴ The requiredcondition is m1(c2-c3) + m2(c3-c1)+ m3(c1-c2) = 0