El concepto Vector

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Definition of a Vector

Definition

A vector is a geometric entity characterized by a magnitude and a length.

It is defined in a coordinate system identifying its origin, which can coincide with the origin of the coordinate system, and the coordinates that mark the direction of the vector.

If each point is assigned a letter, for example to the $A$ origin and to the $B$ destination, the notation used is loved letters with a vector $\vec{AB}$.

If the vector is represented with its beginning at the origin of the system, it can be described by starting the coordinates of its tip $(a_1,a_2,\ldots,a_n)$ in which as many coordinates are used as the system has dimensions.

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Defining a Base

Image

$\hat{n}$

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El concepto Vector

Storyboard

Variables

Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$\vec{a}$
&a
Component of the Vector $\vec{a}$ in $\hat{x}$
m
$\hat{n}$
&n
Componente $\hat{x}$ del Vector resta de $\vec{b}$ de $\vec{a}$
-
$\mid\vec{a}\mid$
a
Magnitud del vector
m
$\vec{b}$
&b
Vector
m
$c_z$
c_z
Vector
m
$\hat{a}_1$
&na_1
Vector
m
$b_y$
b_y
Vector que resulta de la suma
m

Calculations


First, select the equation:   to ,  then, select the variable:   to 

Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
Solved
Translated

 Variable   Given   Calculate   Target :   Equation   To be used



Equations


Examples

A vector is a geometric entity characterized by a magnitude and a length.

It is defined in a coordinate system identifying its origin, which can coincide with the origin of the coordinate system, and the coordinates that mark the direction of the vector.

If each point is assigned a letter, for example to the $A$ origin and to the $B$ destination, the notation used is loved letters with a vector $\vec{AB}$.

If the vector is represented with its beginning at the origin of the system, it can be described by starting the coordinates of its tip $(a_1,a_2,\ldots,a_n)$ in which as many coordinates are used as the system has dimensions.

La suma de dos vectores \vec{a}=(a_x,a_y,a_z) y \vec{b}=(b_x,b_y,b_z) se realiza sumando cada una de las coordenadas:

equation

Un Versor es un Vector de largo unitario. Se le puede calcular de cualquier vector simplemente dividiendo dicho vector por la magnitud de este.

Para diferenciar los versores de los vectores generales no se les dibuja una flecha si no que un tipo de gorro.

Por ello el versor $\hat{a}=(\hat{a}_x,\hat{a}_y,\hat{a}_z)$ calculado del vector $\vec{a}=(a_x,a_y,a_z)$ como:

equation

donde el modulo del vector esta definido en dos dimensiones por

equation=4808

y en tres dimensiones por

equation=4809


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