Q. The three straight lines $ax + by = c,\ bx + cy = a$ and $cx + ay = b$ are collinear, if
A) $b + c = a$
B) $c + a = b$
C) $a + b + c = 0$
D) $a + b = c$
Explanation
(c)
On adding the given three equations, we get
$ax + by + bx + cy + cx + ay = a + b + c$
$\Rightarrow \ (a + b + c)x + (a + b + c)y = (a + b + c)$
On comparing with $0x + 0y = 0$ for collinearity, we get
$a + b + c = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.