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Two mutually orthogonal unit vectors acting at a point $p$, produce a resultant, whereas the two orthogonal unit basis vectors at the origin do not, why?

John Rennie
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pete
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1 Answers1

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Vectors don't act - they're objects, not operators. The action is being done to one vector or the other by the operation of vector concatenation (more commonly "vector addition", which is a perfectly good term since we can express vectors as matrices or algebraic sums, both of which are concatenated with addition, and vector addition follows all the commutative, associative, and identity properties of addition).

If you operate on a basis vector by doing vector addition with another basis vector you get a resultant that's the vector sum of the basis vectors, as you would expect.

Note 1: Vectors also don't have location, although they may describe properties of mathematical objects that do (e.g. a point mass).

Note 2: we often talk about forces acting on objects, which seems (since force is a vector quantity) like it contradicts what I said - but it's just linguistic. When a force acts on an object, what we mean mathematically is that we need a new mathematical object to describe the physical object that having a particular physical interaction whose mathematical counterpart is a force vector.

g s
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