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The lines ix + my + n = 0 , mx + ny + l = 0 and nx + ly +m = 0 are concurrent if
  • a)
    l + m – n = 0
  • b)
    l + m + n = 0
  • c)
    l – m – n = 0
  • d)
    I – m + n = 0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The lines ix + my + n = 0 , mx + ny + l = 0 and nx + ly +m = 0 are con...
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 - l�) - m(m� - nl) + n(ml - n�) = 0
lmn - l� - m� + lmn + lmn - n� = 0
l� + m� + n� = 3lmn
this condition true if an only if
l + m + n = 0      (In case of l ≠  m ≠ n)

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The lines ix + my + n = 0 , mx + ny + l = 0 and nx + ly +m = 0 are concurrent ifa)l + m – n = 0b)l + m + n = 0c)l – m – n = 0d)I – m + n = 0Correct answer is option 'B'. Can you explain this answer?
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The lines ix + my + n = 0 , mx + ny + l = 0 and nx + ly +m = 0 are concurrent ifa)l + m – n = 0b)l + m + n = 0c)l – m – n = 0d)I – m + n = 0Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The lines ix + my + n = 0 , mx + ny + l = 0 and nx + ly +m = 0 are concurrent ifa)l + m – n = 0b)l + m + n = 0c)l – m – n = 0d)I – m + n = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lines ix + my + n = 0 , mx + ny + l = 0 and nx + ly +m = 0 are concurrent ifa)l + m – n = 0b)l + m + n = 0c)l – m – n = 0d)I – m + n = 0Correct answer is option 'B'. Can you explain this answer?.
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