Name: vector components in 3d space
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 28 s
Channel: JoVE

Considere un vector A con sus componentes x e y representados en términos de vectores unitarios, i y j. Aquí los vectores unitarios tienen una magnitud adimensional de uno.
Dado que la magnitud de cualquier componente vectorial es siempre una cantidad positiva, representada por escalares, A se puede expresar como un vector cartesiano.
Aquí, se utiliza un sistema de coordenadas rectangulares a la derecha. El pulgar de la mano derecha apunta hacia el eje z positivo y los dedos se curvan desde el eje x positivo hacia el eje y positivo.
Un vector tridimensional se puede representar en coordenadas cartesianas rectangulares utilizando vectores unitarios i, j y k. La dirección de estos vectores se representa en función de los ejes positivos o negativos.
Un vector se representa como la suma vectorial de sus componentes individuales, y su magnitud se expresa como la raíz cuadrada positiva de la suma de los cuadrados de sus componentes.
Las operaciones de álgebra vectorial se simplifican representando el vector en la forma cartesiana. Separa su magnitud y dirección a lo largo de los ejes utilizando la notación de vector unitario.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 34, 44, 45.</li>
</ol>

notación vectorial cartesiana

La notación vectorial cartesiana es una herramienta valiosa en ingeniería mecánica para representar vectores en el espacio tridimensional, realizar operaciones vectoriales como determinar el gradiente, la divergencia y el rotacional, y expresar cantidades físicas como el desplazamiento, la velocidad, la aceleración y la fuerza. Al utilizar la notación vectorial cartesiana, los ingenieros pueden analizar y resolver problemas más fácilmente en diversas áreas de la ingeniería mecánica, incluyendo la dinámica, la cinemática y la mecánica de fluidos. Esta notación representa un vector en términos de tres componentes a lo largo de los ejes x, y, y z, respectivamente. Por ejemplo, supongamos que tenemos un vector A que apunta en la dirección (3, -4, 5). En ese caso, se puede representar utilizando la notación vectorial cartesiana como A = 3i - 4j + 5k, donde i, j y k son vectores unitarios a lo largo de los ejes x, y, y z, respectivamente. Los vectores unitarios se definen como i = (1, 0, 0), j = (0, 1, 0) y k = (0, 0, 1). La notación vectorial cartesiana se puede utilizar para realizar diversas operaciones vectoriales, como la suma, la resta y la multiplicación por un escalar. Por ejemplo, si tenemos dos vectores, A = 3i - 4j + 5k y B = 2i + 7j - 3k, podemos sumarlos utilizando la notación vectorial cartesiana de la siguiente manera: <img alt="Equation 1" src="/files/ftp_upload/14232/14232_ Equation_1v2.svg" style="text-align: center; height: 13px;"> También podemos restarlos de la siguiente manera: <img alt="Equation 2" src="/files/ftp_upload/14232/14232_ Equation_2v2.svg" style="text-align: center; height: 13px;">

Notación vectorial cartesiana

La notación vectorial cartesiana es una herramienta valiosa en ingeniería mecánica para representar vectores en un espacio tridimensional, realizar operaciones vectoriales ...

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Force Vectors

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KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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vector components in 3d space

Cartesian vector notation shows how to write vectors in three-dimensional space using x, y, and z components. It gives a clear way to represent direction and size for quantities used in mechanical engineering.

The notation uses the unit vectors i, j, and k for the x, y, and z axes. A vector pointing in the direction (3, −4, 5) can be written as A = 3i - 4j + 5k. The unit vectors are i = (1, 0, 0), j = (0, 1, 0), and k = (0, 0, 1).

This form is useful for describing displacement, velocity, acceleration, and force. It also helps engineers work with dynamics, kinematics, and fluid mechanics. Cartesian vector notation can also support vector operations such as addition, subtraction, and scalar multiplication.

The same notation is also used with gradient, divergence, and curl. These operations are important in mechanical engineering calculations. For example, two vectors such as A = 3i - 4j + 5k and B = 2i + 7j - 3k can be added or subtracted using their components.

Vector Components in 3D Space

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Learn how Cartesian vector notation uses i, j, and k to show 3D vectors, describe force and motion, and perform addition, subtraction, and scalar multiplication.

Vector Components in 3D Space | 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.

mechanical engineering

Vector Components in 3D Space

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