For vectors a, b, c in ℝ3, the vector triple product is a × (b × c). The use of brackets here is essential, since (a × b) × c, another vector triple product, gives, in general, quite a different result. The vector a × (b × c) is perpendicular to b × c and so lies in the plane determined by b and c. In fact, a × (b × c) = (a. c)b − (a. b)c.