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Definition of a Vector
Description
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.
ID:(706, 0)
Vector Addition (3D)
Equation
La suma de dos vectores
| $( c_x , c_y , c_z )=( a_x + b_x , a_y + b_y , a_z + b_z )$ |
ID:(3670, 0)
Versor (3D)
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:
| $( \hat{a}_x , \hat{a}_y , \hat{a}_z )=\left(\displaystyle\frac{ a_x }{ \mid\vec{a}\mid },\displaystyle\frac{ a_y }{ \mid\vec{a}\mid },\displaystyle\frac{ a_z }{ \mid\vec{a}\mid }\right)$ |
donde el modulo del vector esta definido en dos dimensiones por
| $ \mid\vec{a}\mid =\sqrt{ a_x ^2+ a_y ^2}$ |
y en tres dimensiones por
| $ \mid\vec{a}\mid =\sqrt{ a_x ^2+ a_y ^2+ a_z ^2}$ |
ID:(3674, 0)