Straight Line Question 38

Question: If the lines $ ax+by+c=0 $ , $ bx+cy+a=0 $ and $ cx+ay+b=0 $ be concurrent, then [IIT 1985; DCE 2000, 02]

Options:

A) $ a^{3}+b^{3}+c^{3}+3abc=0 $

B) $ a^{3}+b^{3}+c^{3}-abc=0 $

C) $ a^{3}+b^{3}+c^{3}-3abc=0 $

D)None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • Here the given lines are $ ax+by+c=0 $ …..(i) $ bx+cy+a=0 $ …..(ii) $ cx+ay+b=0 $ …..(iii) The lines will be concurrent, if $ | \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} |=0 $
    Þ $ a^{3}+b^{3}+c^{3}-3abc=0 $ .