Name: cross product direction and magnitude
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 25 s
Channel: JoVE

O produto cruzado é um produto de dois vetores diferentes cujo resultante é um terceiro vetor.
A magnitude do produto vetorial é obtida multiplicando a magnitude dos vetores e o seno do ângulo entre eles.
Aqui, a magnitude do produto vetorial pode ser multiplicada por um vetor unitário que especifica a direção do vetor resultante.
A regra da mão direita fornece a direção do vetor resultante. Se os dedos enrolados representam a direção do vetor A para o vetor B, então a direção do polegar representa a direção do vetor resultante.
O vetor resultante é sempre perpendicular ao plano que contém os vetores A e B.
O produto cruzado dos vetores não é comutativo. A resultante do produto vetorial do vetor A com o vetor B é igual em magnitude, mas oposta em direção à do produto vetorial do vetor B com o vetor A.
No entanto, o produto cruzado obedece às leis associativas e distributivas.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 125 a 126.</li>
</ol>

produto vetorial

Cross Product

O produto vetorial é um conceito fundamental na álgebra vetorial que é uma operação vetorial em dois vetores diferentes para obter um terceiro vetor. Ao contrário do produto escalar, o produto vetorial resulta em uma quantidade vetorial perpendicular aos vetores originais.

A magnitude do produto vetorial é obtida multiplicando a magnitude de ambos os vetores e o seno do ângulo entre eles. Isso significa que um ângulo maior entre os vetores levará a uma magnitude maior do produto vetorial.

<img alt="Equation 1" src="/files/ftp_upload/14251/14251_Equation_1v3.svg" style="text-align: center; height: 11px;" />

A direção do vetor resultante é determinada pelo uso da regra da mão direita. Se enrolarmos os dedos da mão direita do vetor A ao vetor B, então a direção do polegar representa a direção do vetor resultante. Em outras palavras, a direção do produto vetorial é perpendicular ao plano que contém os vetores A e B.

É importante observar que o produto vetorial de vetores é não comutativo. Ou seja, o vetor resultante para o produto vetorial do vetor A com o vetor B é igual em magnitude, mas oposto em direção ao produto vetorial do vetor B com o vetor A. No entanto, o produto vetorial obedece à lei associativa e às leis distributivas de adição. Isso significa que o produto vetorial de uma soma de vetores é igual à soma dos produtos vetorials de cada vetor.

Em conclusão, o produto vetorial é um conceito fundamental na álgebra vetorial que tem aplicações amplas em física e engenharia, como calcular o momento de uma força em relação a um ponto, calcular o torque de uma força em relação a um eixo e calcular o momento angular de um corpo em relação a um eixo.

Produto Vetorial

O produto vetorial é um conceito fundamental em álgebra vetorial que é uma operação vetorial em dois vetores diferentes para obter um terceiro vetor. Ao contrário do ...

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cross product direction and magnitude

The cross product is a vector operation in vector algebra that creates a third vector from two input vectors. Unlike the scalar product, it does not give a single number. The result is a vector perpendicular to both original vectors.

The size, or magnitude, of the cross product depends on the magnitudes of both vectors and the sine of the angle between them. A larger angle between the vectors gives a larger cross product magnitude. The direction is found with the right-hand rule. If the fingers of the right hand curl from vector A to vector B, the thumb shows the direction of the result.

The cross product points perpendicular to the plane containing vectors A and B. It is also non-commutative. That means A cross B has the same magnitude as B cross A, but the direction is opposite.

The cross product still follows the associative law and the distributive law of addition. So, the cross product of a sum of vectors equals the sum of the cross products of each vector. This idea is useful in physics and engineering. It is used to calculate the moment of a force about a point, torque about an axis, and angular momentum about an axis.

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Cross Product Direction and Magnitude

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