Why vector form is convenient?

  1. I read that a point relative to origin in 3D coordinate system is conveniently specified by the vector form, why?
     
  2. jcsd
  3. arildno

    arildno 12,015
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    Because
    a) the vectorial description contains all the info required to identify the point, and nothing superfluous
    b) The manner in which we write vectors makes it easy for us to treat them as a type of numbers; that is, we easily see how to add, and for that matter (sort of) multiply them together, and also how to interpret, in a geometric sense, what such algebraic operations "really" means.
     
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  4. HallsofIvy

    HallsofIvy 40,663
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    Because there are many different points the same distance from the origin (or any one point) of a coordinate system so a single number will not suffice to identify it. Equivalently, it take 3 numbers to identify everypoint in a 3D coordinate system (pretty much the definition of "3D") and it is convenient to arrange those numbers in an array. It is the fact, from geometry of similar triangles, that the coordinates [itex](x_0, y_0, z_0)[/itex] of a point exactly 1/2 way between two points [itex](x_1, y_1, z_1)[/itex] and [itex](x_2, y_2, z_2)[/itex] are [itex](x_0, y_0, z_0)= ((x_1+ x_2)/2, (y_1+ y_2)/2, (z_1+ z_2)/2)[/itex] that means that "scalar multiplication" of vectors is convenient (in fact, "scalar multiplication" and the whole idea of vectors was created to simplify that).

    (Arildno got in two minutes before me! And we are saying essentially the same thing.)
     
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  5. got it, Thank you both for clarifying my doubt
     
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