The three straight lines \( \Large ax+by=c,\ bx+cy=a\ and\ cx+ay=b \) are collinear if:

A) \( \Large a+b+c = 0 \)
B) \( \Large c+a=b \)

C) \( \Large b+c=a \)
D) \( \Large a+b=c \)

Correct answer:
A) \( \Large a+b+c = 0 \)

Description for Correct answer:
We have \( \Large ax+by=c \) ...(i)

\( \Large bx+cy=a \) ...(ii)

and \( \Large cx+ay=b \) ...(iii)

On adding equation (i), (ii) and (iii), we get

\( \Large ax+by+bx+cy+cx+ay = a+b+c \)

=> \( \Large \left(a+b+c\right)x+ \left(a+b+c\right)y = \left(a+b+c\right) \)

On comparing with \( \Large ox+oy=0 \) (for collinearity)

We get\( \Large a+b+c = 0 \)

Please provide the error details in above question

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