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Physics[Vectors][Component] - the component (first, second, or third) of a vector
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Calling Sequence
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Component(A, n)
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Parameters
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A
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an algebraic vector
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n
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a name or one of 1, 2, 3, or an algebraic expression representing these numbers
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Description
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Component(A, n) returns the nth. component of the vector A when A is a projected vector expression, or an unevaluated representation of the nth component when A is a non-projected vector or n is an unresolved name representing one of 1, 2 or 3. If A is not a vector then an error message is returned. Regarding how a vector is identified as such in the context of the Physics/Vectors package, see Identify and type, PhysicsVectors.
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The %Component is the inert form of Component, that is: it represents the same mathematical operation while holding the operation unperformed. To activate the operation use value.
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When Component returns unevaluated, the display on the screen shows the vectorial expression between parentheses, and indexed (as usual when working by hand). This is done using a `print/Component` procedure.
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Examples
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![with(Physics[Vectors])](/support/helpjp/helpview.aspx?si=4898/file06387/math94.png)
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![[`&x`, `+`, `.`, ChangeBasis, Component, Curl, DirectionalDiff, Divergence, Gradient, Identify, Laplacian, Nabla, Norm, Setup, VectorDiff]](/support/helpjp/helpview.aspx?si=4898/file06387/math97.png)
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![[mathematicalnotation = true]](/support/helpjp/helpview.aspx?si=4898/file06387/math104.png)
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An explicit algebraic vector in cartesian coordinates
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The first and third components
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The "nth" component returns unevaluated
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Substituting n by something concrete, the component is obtained
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Here A_ is an abstract non-projected vector; by default, in the framework of the Physics[Vectors] package, symbols ending with "_" represent non-projected vectors (to change this postfix see Setup:
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The second component
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When  is replaced by a projected vector, the selection of the component is performed
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It is also possible to work all abstract; this is the "nth" component of a non-projected vector
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Component admits as argument a generic algebraic vectorial expression, for instance
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Note however that when the expression passed to Component is not a vector, the computation is interrupted with an error message
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