This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
 Mathematica Tutorial Functions »

Vector Operations

 v[[i]] or Part[v,i] give the ith element in the vector v c v scalar multiplication of c times the vector v u.v dot product of two vectors Norm[v] give the norm of v Normalize[v] give a unit vector in the direction of v

Basic vector operations.

This is a vector in three dimensions.
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This gives a vector u in the direction opposite to v with twice the magnitude.
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This reassigns the first component of u to be its negative.
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This gives the dot product of u and v.
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This is the norm of v.
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This is the unit vector in the same direction as v.
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This verifies that the norm is 1.
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Two vectors are orthogonal if their dot product is zero. A set of vectors is orthonormal if they are all unit vectors and are pairwise orthogonal.
 Projection[u,v] give the orthogonal projection of u onto v Orthogonalize[{v1,v2,...}] generate an orthonormal set from the given list of vectors

Orthogonal vector operations.

This gives the projection of u onto v.
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p is a scalar multiple of v.
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u-p is orthogonal to v.
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Starting from the set of vectors {u, v}, this finds an orthonormal set of two vectors.
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When one of the vectors is linearly dependent on the vectors preceding it, the corresponding position in the result will be a zero vector.
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