Given:
m1x – y + c1 = 0 … (1)
m2x – y + c2 = 0 … (2)
m3x – y + c3 = 0 … (3)
It is given that the three lines are concurrent.
Now, consider the following determinant:
m1(-c3 + c2) + 1(m2c3 - m3c2) + c1(-m2 + m3) = 0
m1(c2 - c3) + m2(c3 - c1) + m3(c1 - c2) = 0
∴ The required condition is m1(c2 - c3) + m2(c3 - c1) + m3(c1 - c2) = 0
