Question

the lines lx+my+n=0, mx+ny+l=0 and nx+ly+m=0 are concurrent if

Answer 1

Answer:

l + m + n = 0   option (1)

Explanation:

Suppose we have three straight lines whose equations are:

a₁x + b₁y + c₁ = 0,

a₂x + b₂y + c₂ = 0

a₃x + b₃y + c₃ = 0.

These lines are said to be concurrent if the following condition holds:

Determinant of

a₁     b₁     c₁

a₂     b₂     c₂   =  0

a₃     b₃     c₃

Now

l     m     n

m     n     l      =   0

n     l     m

l(nm - l²) - m(m² - nl) + n(ml - n²) = 0

lmn - l³ - m³ + lmn + lmn - n³ = 0

l³ + m³ + n³ = 3lmn

this condition true if an only if

l + m + n = 0      (In case of l ≠  m ≠ n)

Answer 2

Step-by-step explanation:

the final condition will be true if l+m+n=0