[CuervO]

Quote:

Originally Posted by Rajat_Pawar Thanks for the rest, but AFAIK - this is wrong.

That means my university engineering textbook for Mathematician Analysis I is wrong?!!; You basically use Pythagorean theorem; I'm not trying to be an smart ass, this guide is incredibly useful, but.... you know.

Module, Absolute, Length, are all synonims and that's what that formula gets.

Taken straight from the book:

There are physical properties which to be measured it is necessary to define it's direction, intensity and some times point of origin. These kind of magnitudes are called vectorians and they can be sorted in oriented segments. Among them we can mention the magnitudes of force, velocity, acceleration, etc.

Each one of these oriented segments receive the name of vectors. They are represented geometrically as rectal segments directed in the three different spaces.

Given a point P ∈ ℝ and a point O ∈ ℝ, we will cover the trhee dimensions:

Unidimensional vectors:

Code:

       i
  ------>------------------------- X
O                                   P

→ OP = Xp (Xp ∈ ℝ)
(X ∈ ℝ) is defined as component X of a vector.

→ |OP| = √(A)І
Which is redundant

--

Bidimensional Vectors




→ OP = Xp i + Yp j ⇔ (Xp, Yp) ⇔ (Xp ^ Yp defined as components)
(X,Y ∈ ℝ)

To calculate the module of this vector we apply Pythagorean theorem:
→ |OP| = √( (Xp)І + (Yp)І )

--

Tridimensional vector (Can't really reproduce the vector position so let's just make a square out of it that represents the OP vector)



→ OP = Xp i + Yp j + Zp k ⇔ (Xp, Yp, Zp) ⇔ (Xp ^ Yp ^ Zp defined as components).
(X,Y,Z ∈ ℝ)

Module:
→ |OP| = √((Xp)І + (Yp)І + (Zp)І)


onclusions:

- A vector (→) is used to measure magnitudes which requiere direction and intensity.
- The intensity of a vector (module |→|) is the sum of all it's components powered to the second and then root squared again.
- It's direction will be determined by it's symbol (+,-)
- There's a versor (aka unit vector) which will share the direction of the vector and will have a module of 1
(|i| = 1, |k| = 1, |j| = 1)


Counter examples.

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Unit vectors, namely i, j & k, are vectors in the direction of the X, Y & Z axes respectively of magnitude 1 unit.

Their length is not always 1 unit. Their module is.

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A vector is represented using unit vectors.

Not always, as shown previously.

Quote:

A vector's magnitude is - SquareRoot( (a * a) + (b * b) + (c * c) )

A vector magnitude is what it is measuring. A vector's magnitude can either be force, direction, intensity, etc. What you calculate by that is it's module against the origin, that's why the examples used OP, O stands for Origin and P for Point. Origin is threated as the origin of coordinates within the cartesian axis map (Ordered Triplet (0,0,0)); you can calculate different modules by using the differences.

You can see that →O = →(0,0,0) there for it wont affect the module.
If →O where to be anything else, for example: →O = →(15,-14,2) then the differences between the point and the origin must be calculated.

√((Xp-Xo)І + (Yp-Yo)І + (Zp-Zo)І)
(X,Y,Z ∈ ℝ)

Once again, I am not trying to prove myself smartass but there are missconceptions which on a deep level could mess your methods completely. For this guide this shouldn't even be worth mentioning, but it is always great to learn something new!