Let a , b and c be distinct positive numbers. If the vectors a i ^ + a j ^ + c k ^ , i ^ + k ^ and c i ^ + c j ^ + b k ^ are co-planar, then c is equal to:

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Given vectors a i ^ + a j ^ + c k ^ , i ^ + k ^ and c i ^ + c j ^ + b k ^ are co-planar, then a a c 1 0 1 c c b = 0 ⇒ a 0 - c - a b - c + c c - 0 = 0 ⇒ c 2 = a b ⇒ c = a b .

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