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

Considere um vetor A com seus componentes x e y representados em termos de vetores unitários, i e j. Aqui, os vetores unitários têm magnitude adimensional de um.
Como a magnitude de qualquer componente vetorial é sempre uma quantidade positiva, representada por escalares, A pode ser expressa como um vetor cartesiano.
Aqui, um sistema de coordenadas retangular destro é usado. O polegar da mão direita aponta para o eixo z positivo e os dedos se curvam do eixo x positivo em direção ao eixo y positivo.
Um vetor tridimensional pode ser representado em coordenadas cartesianas retangulares usando vetores unitários i, j e k. A direção desses vetores é representada dependendo dos eixos positivo ou negativo.
Um vetor é representado como a soma vetorial de seus componentes individuais, e sua magnitude é expressa como a raiz quadrada positiva da soma dos quadrados de seus componentes.
As operações de álgebra vetorial são simplificadas pela representação do vetor na forma cartesiana. Ele separa sua magnitude e direção ao longo dos eixos usando notação vetorial unitária.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pp. Página nº 34, 44, 45.</li>
</ol>

notação vetorial cartesiana

A notação vetorial cartesiana é uma ferramenta valiosa na engenharia mecânica para representar vetores no espaço tridimensional, realizar operações vetoriais como determinar o gradiente, divergência e rotacional, e expressar grandezas físicas como deslocamento, velocidade, aceleração e força. Usando a notação vetorial cartesiana, os engenheiros podem analisar e resolver problemas mais facilmente em várias áreas da engenharia mecânica, incluindo dinâmica, cinemática e mecânica dos fluidos. Essa notação representa um vetor em termos de três componentes ao longo dos eixos x, y, e z, respectivamente.

Por exemplo, suponha que tenhamos um vetor A apontando na direção (3,−4, 5). Nesse caso, ele pode ser representado usando a notação vetorial cartesiana como A = 3i - 4j + 5k, onde i, j e k são vetores unitários ao longo dos eixos x, y, e z, respectivamente. Os vetores unitários são definidos como i = (1, 0, 0), j = (0, 1, 0) e k = (0, 0, 1).

A notação vetorial cartesiana pode ser usada para realizar diversas operações vetoriais, como adição, subtração e multiplicação por escalar. Por exemplo, se tivermos dois vetores, A = 3i - 4j + 5k e B = 2i + 7j - 3k, podemos adicioná-los usando a notação vetorial cartesiana da seguinte forma:

<img alt="Equation 1" src="/files/ftp_upload/14232/14232_ Equation_1v2.svg" style="text-align: center; height: 13px;" />

Também podemos subtraí-los da seguinte maneira:

<img alt="Equation 2" src="/files/ftp_upload/14232/14232_ Equation_2v2.svg" style="text-align: center; height: 13px;" />

Notação Vetorial Cartesiana

A notação vetorial cartesiana é uma ferramenta valiosa em engenharia mecânica para representar vetores no espaço tridimensional, realizar operações vetoriais ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force Vectors

Vetores de Força

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Cartesian Vector Notation

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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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,...

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Vector Components in 3D Space | JoVE K12

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Vector Components in 3D Space

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