Post by chemguy
Reference; http://newstuff77.weebly.com 31 The Fine Structure Vector
Not even wrong.
[I am using abbreviated LaTeX below to fit your formatting as best as
| Force may be represented as a 3D vector (vec F);
| vec F = F_11 vec i + F_12 vec j + F_13 vec k
[You should have used colon instead of semicolon; corrected below.]
| Where […] vec i, vec j, vec k are directional vectors in 3D (unit vectors)
Those are called _base_ vectors instead.
| F_11, F_12, F_13 are components of force
They are components _of the_ force _vector_, then.
| The vector has magnitude: |vec F| = F_14
One can make that definition, but it implies, *falsely*, that the magnitude
of a vector is one of its intrinsic components. The magnitude (norm) of a
vector is defined by the used metric instead.
| The components are related to the magnitude:
| (F_11)^2 + (F_12)^2 + (F_13)^2 = (F_14)^2
Only with a _Euclidean_ metric, and even then the magnitude is NOT a
component of the vector itself. That would be a recursive definition
because the magnitude of a vector is based on its components.
| A fourth component (F_10) is:
| (F_10)^2 = (F_11)^2 + (F_12)^2 = (F_14)^2 - (F_13)^2
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