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Unformatted text preview: Vector algebra. Combining two changes of position corresponds to adding components. Vectors can also be subtracted, and there is a ~ 0 vector. Multiplying vectors by numbers other than 1 rescales the vectors and sometimes reverses them. Vector algebra has many of the properties of algebra with numbers. Magnitude and direction. The length of a vector is the squareroot of the sum of the squares of its (standard) components. Each vector, except ~ 0, can be factored in the form ~ b = b ˆ b , where the number b is the magnitude of the vector ~ b , and the unit vector ˆ b gives the direction of ~ b . Standard basis vectors. All vectors in R 3 are linear combinations of the unit vectors ˆ i , ˆ j and ˆ k . The End 8 January 2007...
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 Spring '03
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 Linear Algebra, Vectors, Standard basis

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