Name: adding and multiplying vectors
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 20 s
Channel: JoVE

Considere dois vetores de força em um sistema de coordenadas bidimensional.
Esses vetores podem ser adicionados usando a lei do paralelogramo, onde as caudas dos vetores concorrentes são unidas e as linhas paralelas a cada vetor são desenhadas para formar um paralelogramo.
O vetor resultante pode ser obtido desenhando uma diagonal das caudas até o ponto de interseção das linhas.
Da mesma forma, os vetores podem ser adicionados usando a regra do triângulo, onde dois vetores são organizados como dois lados do triângulo unidos cabeça-a-cauda, e o terceiro lado do triângulo representa a magnitude e a direção do vetor resultante.
A subtração vetorial é semelhante à adição reversa de um vetor a outro. Como resultado, a diferença entre dois vetores é obtida usando as mesmas regras de adição de vetores.
Quando um vetor é multiplicado por um escalar, a magnitude do vetor varia de acordo com a quantidade escalar.
Se o escalar for positivo, a direção do vetor permanecerá a mesma e, se for negativa, a direção será invertida.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. págs. 18 -19</li>
</ol>

operações com vetores

Vetores são quantidades físicas que possuem magnitude e direção. As operações com vetores incluem adição, subtração e multiplicação escalar.

Um vetor multiplicado por um valor escalar é chamado de multiplicação escalar. O resultado obtido é um novo vetor com uma magnitude diferente. Se o escalar for positivo, a direção do vetor permanece a mesma, mas, se for negativo, a direção do vetor é invertida. Por exemplo, o produto da massa e velocidade resulta no momento. Aqui, a quantidade escalar massa é multiplicada pela quantidade vetorial velocidade, o que resulta na quantidade vetorial momento. A direção do vetor momento resultante é na mesma direção do vetor velocidade.

Os dois vetores podem ser adicionados geometricamente utilizando a lei do paralelogramo da adição de vetores. Quando adicionados usando essa lei, os dois vetores são representados como lados adjacentes de um paralelogramo. As caudas de ambos os vetores são colocadas na origem e as linhas paralelas a cada vetor são desenhadas para formar um paralelogramo. A diagonal do paralelogramo é então desenhada da origem até o canto oposto do paralelogramo para representar o vetor resultante. A magnitude e direção do vetor resultante podem ser determinadas medindo o comprimento e os ângulos da diagonal do paralelogramo. A lei do paralelogramo pode ser simplificada em um cenário especial onde ambos os vetores são colineares, ou seja, possuem a mesma linha de ação. Nesse caso, o vetor resultante pode ser obtido através da adição algébrica ou escalar dos dois vetores.

Outro método de adicionar dois vetores graficamente é a lei do triângulo da adição de vetores. A regra do triângulo da adição de vetores afirma que, se dois vetores forem dispostos juntos, com uma extremidade ligada à outra, como dois lados de um triângulo, o terceiro lado do triângulo representa a magnitude e direção do vetor resultante. A adição de vetores utilizando essa lei envolve colocar o primeiro vetor na origem e colocar o segundo vetor com uma extremidade ligada à extremidade oposta do primeiro vetor. O terceiro lado do triângulo da origem até o final do segundo vetor representa o vetor resultante.

O processo de subtração de vetores envolve adicionar o inverso (negativo) de um vetor a outro vetor. Isso significa que as regras de adição de vetores podem ser aplicadas para obter a diferença entre os dois vetores.

Operações com vetores

Vetores são grandezas físicas que têm magnitude e direção. As operações vetoriais incluem adição, subtração e multiplicação escalar.
Um...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force Vectors

Vetores de Força

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Vector Operations

adding and multiplying vectors

Vectors are quantities with both magnitude and direction, and their operations include addition, subtraction, and scalar multiplication. Scalar multiplication means a vector is multiplied by a scalar value, which creates a new vector with a different magnitude. If the scalar is positive, the direction stays the same. If the scalar is negative, the direction reverses.

A common example is momentum, which comes from multiplying mass by velocity. In this case, mass is the scalar quantity and velocity is the vector quantity. The result is momentum, and its direction matches the direction of the velocity vector.

Two vectors can be added geometrically with the parallelogram law. In this method, the two vectors are drawn as adjacent sides of a parallelogram with both tails at the origin. Lines are then drawn parallel to each vector to complete the shape.

The diagonal of the parallelogram, drawn from the origin to the opposite corner, shows the resultant vector. Its magnitude and direction can be found by measuring the diagonal's length and angles. When the two vectors are collinear, meaning they share the same line of action, the resultant can be found by algebraic or scalar addition.

Another way to add vectors is the triangle law of vector addition. Here, the vectors are arranged head to tail as two sides of a triangle. The third side of the triangle, from the origin to the end of the second vector, represents the resultant vector.

Vector subtraction uses the reverse, or negative, of one vector added to another vector. This lets the rules of vector addition be used to find the difference between two vectors.

Adding and Multiplying Vectors

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vector operations

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key terms and concepts

Learn how vector addition, subtraction, and scalar multiplication work using parallelogram and triangle laws, plus a momentum example for high school science.

Adding and Multiplying Vectors | JoVE K12

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

mechanical engineering

Adding and Multiplying Vectors

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