If a × b = a × c and a ≠ 0, then which of the following is definitely true?

If a × b = a × c and a ≠ 0, then which of the following is definitely true?

• A. b = c
• B. a is parallel to (b − c)
• C. b is parallel to c
• D. a is perpendicular to (b − c)

Answer: B) a is parallel to (b − c)

Explanation: a × b − a × c = 0 → a × (b − c) = 0. This means that either b − c = 0 (so b = c), or vector a is parallel to vector (b − c). Thus, b=c is not 'definitely' true, but a being parallel to (b−c) encompasses the general relationship (including the zero vector case trivially).