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For any three vectors a, b and c (a – b) . (b + c) × (c + a) is equal to

For any three vectors a, b and c (a – b) . (b + c) × (c + a) is equal to Correct Answer 0

(a – b). (b + c) × (c + a)

= (a – b) . (b × c + b × a + c × c + c × a)

= (a – b) . (b × c + b × a + c × a)

= a.(b × c) + a.(b × a) + a.(c × a) – b.(b × c) - b.(b × a) – b.(c × a)

= a.(b × c) – b.(c × a)

= –

= – = 0

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