Unformatted text preview: the cross product of two vectors is always a vector . ~u × ~v = ± ± ± ± ± ± ˆ ı ˆ ˆ k u 1 u 2 u 3 v 1 v 2 v 3 ± ± ± ± ± ± = ± ± ± ± u 2 u 3 v 2 v 3 ± ± ± ± ˆ ı± ± ± ± u 1 u 3 v 1 v 3 ± ± ± ± ˆ + ± ± ± ± u 1 u 2 v 1 v 2 ± ± ± ± ˆ k ~u × ~v =~v × ~u ~u × ~v = 0 ⇔ ~u k ~v  ~u × ~v  =  ~u  ~v  cos θ The direction of ~u × ~v is perpendicular to both ~u and ~v , oriented according to the righthand rule. The magnitude  ~u × ~v  is equal to the area of the parallelogram spanned by ~u and ~v . Equation for a plane: ~ N · ( ~ r~ r ) = 0...
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 Spring '07
 McClain
 Math, Calculus, Vector Space, Dot Product, Cos

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