the lines lx+my+n=0, mx+ny+l=0 and nx+ly+m=0 are concurrent if
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35
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)
Answered by
4
Step-by-step explanation:
the final condition will be true if l+m+n=0
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