BITSAT 2012 Paper

a. b. = a.c ⇒ a.(b – c) = 0
⇒ a = 0 or b – c = 0 or a ⊥ (b – c)
⇒ a = 0 or b = c or a ⊥ (b – c) ...(1)
Also a x b = a x c ⇒ a × (b – c) = 0
⇒ a = 0 or b – c = 0 or a || (b – c)
⇒ a = 0 or b = c or a || (b – c) ...(2)
Observing to (1) and (2) we find that
a = 0 or b = c