Straight Line Question 56

Question: The three straight lines $ ax+by=c,bx+cy=a $ and $ cx+ay=b $ are collinear, if [MP PET 2004]

Options:

A) $ a+b+c=0 $

B) $ b+c=a $

C) $ c+a=b $

D) $ a+b=c $

Show Answer

Answer:

Correct Answer: A

Solution:

  • Given three straight lines $ ax+by-c=0 $ , $ bx+cy-a=0 $ , $ cx+ay-b=0 $ are collinear,Then $ | \begin{matrix} a & b & -c \\ b & c & -a \\ c & a & -b \\ \end{matrix} |=0 $

$ \Rightarrow $ $ -(a+b+c)| \begin{matrix} 1 & b & c \\ 1 & c & a \\ 1 & a & b \\ \end{matrix} |=0 $ Clearly, $ (a+b+c)=0 $