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Unformatted text preview: ( a , b , c ) , we just need to compute the distance between the origin and the point ( a , b , c ) . (The idea is the same in two dimensions). Our measurement will yield a scalar value of magnitude without direction--not another vector! This type of scalara sounds like the kind of meaningful information the dot product could provide for us. Summary of Dot Product Rules In summary, the rules for the dot products of 2- and 3-dimensional vectors in terms of components are: u v = u 1 v 1 + u 2 v 2 u v = u 1 v 1 + u 2 v 2 + u 3 v 3 The rule for vectors given in terms of magnitude and direction (in either 2 or 3 dimensions), where denotes the angle between them, is: v w = | v || w | cos...
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- Fall '10