Name: using position vectors to locate points
Uploaded: 2025-05-22T09:06:01.000Z
Duration: 1 min 29 s
Channel: JoVE

Un vector de posición es un vector fijo que ubica la posición de un punto en el espacio en relación con otro punto.
Considere un ojo de tornillo fijado a una pared y un cable OP conectado a él. Establezca un sistema de coordenadas cartesianas con ojo de tornillo en el origen y los vectores componentes a lo largo de los ejes para ubicar el punto P en el cable.
Un vector de posición r dirigido desde el origen hasta el punto P se puede expresar en forma de vector cartesiano.
Para una representación general de un vector cartesiano, considere un soporte fijado en una pared y una cuerda unida a él.
Sean nA y nB los vectores de posición que se extienden desde el origen hasta los puntos A y B.
Por lo tanto, el vector de posición resultante n desde el punto A hasta el B, se puede obtener utilizando la regla del triángulo y expresando nA y nB en la forma vectorial cartesiana.
i, j y k son los vectores unitarios a lo largo de las componentes del vector de posición n formado por restar las coordenadas de A de B.

<ol>
	<li>Russell C. Hibbeler. (2016). Ingeniería Mecánica: Estática y Dinámica. Pearson. (Pág. Nº – 56,57)</li>
</ol>

vectores de posición

Un vector de posición es un concepto fundamental en matemáticas que ayuda a determinar la posición de un punto con respecto a otro punto en el espacio. Es un vector que describe la dirección y la distancia entre dos puntos. Los vectores de posición son muy útiles en el campo de las matemáticas y la ciencia, ya que ayudan a representar relaciones espaciales y facilitan los cálculos. 

Por ejemplo, queremos localizar un punto P(x, y, z) en relación con el origen de coordenadas O. En ese caso, podemos definir un vector de posición r, que se extiende desde el origen O hasta el punto P. Podemos expresar este vector en forma de vector cartesiano como: r = xi + yj + zk, donde i, j y k son los vectores unitarios en las direcciones x, y, z, respectivamente. El vector de posición r nos da la dirección y magnitud del vector desde el punto O hasta el punto P. 

Consideremos un vector de posición dirigido desde el punto A al punto B en el espacio. Este vector puede ser denotado por el símbolo r. También podemos referirnos a este vector con dos subíndices para indicar los puntos desde y hacia los cuales está dirigido. Por lo tanto, también podemos designar r como rAB. Por favor, tenga en cuenta que si los vectores de posición se extienden desde el origen de coordenadas, entonces se les llama solo con un subíndice, como rA y rB. El vector de posición rAB se puede obtener a partir de rA y rB usando la expresión rAB = rB - rA = (xB - xA)i + (yB - yA)j + (zB - zA)k. 

Por ejemplo, para establecer un vector de posición desde el punto A hasta B, se restan las coordenadas de la cola A(1 m, 0 m, -3 m) de las coordenadas de la cabeza B(-2 m, 2 m, 3 m), lo que nos da rAB = {-3i + 2j + 6k} m.

Vectores de posición

Un vector de posición es un concepto fundamental en matemáticas que ayuda a determinar la posición de un punto con respecto a otro punto en el espacio. Se trata de un ...

Education

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JoVE Core

Mechanical Engineering

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using position vectors to locate points

Position vectors are used to locate points in space and show the direction and distance between two points. In math and science, they help describe spatial relationships and make calculations easier. A position vector can connect one point to another point or show a point’s location relative to the origin of coordinates.

For a point P(x, y, z) relative to the origin O, the position vector r runs from O to P. In Cartesian vector form, it is written as r = x i + y j + z k. Here, i, j, and k are unit vectors in the x, y, and z directions.

The vector r gives both the direction and the magnitude of the path from O to P. When a vector points from point A to point B, it may be written as rAB. Position vectors from the origin use one subscript only, such as rA and rB.

A vector from A to B can be found by subtracting the coordinates of A from the coordinates of B. The relation is rAB = rB - rA = (xB - xA)i + (yB - yA)j + (zB - zA)k. For example, if A is (1 m, 0 m, -3 m) and B is (-2 m, 2 m, 3 m), then rAB = {-3 i + 2 j + 6 k} m.

Using Position Vectors to Locate Points

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Learn how position vectors locate points in space, use i, j, k notation, and calculate a vector from one point to another with a clear example.

Using Position Vectors to Locate Points | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Using Position Vectors to Locate Points

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