Correct Answer: 4(a ² + b ² + c ² )

Solution : a + b + c=0
⇒ a + b = –c --------------(i)
⇒ b + c = –a --------------(ii)
⇒ c + a = –b --------------(iii)
Substituting (i), (ii) and (iii) in (a + b – c) ² + (b + c – a) ² + (c + a – b) ² , we get
(a + b – c) ² + (b + c – a) ² + (c + a – b) ²
= (–c –c) ² + (–a –a) ² + ( –b –b) ²
= 4c ² + 4a ² + 4b ²
= 4(a ² + b ² + c ² )
Hence, the correct answer is 4(a ² + b ² + c ² ).