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

El producto cruzado es un producto de dos vectores diferentes cuya resultante es un tercer vector.
La magnitud del producto cruzado se obtiene multiplicando la magnitud de ambos vectores y el seno del ángulo entre ellos.
Aquí, la magnitud del producto cruzado se puede multiplicar por un vector unitario que especifica la dirección del vector resultante.
La regla de la derecha da la dirección del vector resultante. Si los dedos curvados representan la dirección del vector A al vector B, entonces la dirección del pulgar representa la dirección del vector resultante.
El vector resultante siempre es perpendicular al plano que contiene los vectores A y B.
El producto cruzado de los vectores no es conmutativo. La resultante del producto cruzado del vector A con el vector B es igual en magnitud pero opuesta en dirección a la del producto cruzado del vector B con el vector A.
Sin embargo, el producto cruzado obedece a las leyes asociativas y distributivas.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 125 \u2012 126.</li>
</ol>

producto cruz

Cross Product

El producto cruz es un concepto fundamental en álgebra vectorial que es una operación de vectores en dos vectores diferentes para obtener un tercer vector. A diferencia del producto escalar, el producto cruz resulta en una cantidad vectorial perpendicular a ambos vectores originales. La magnitud del producto cruz se obtiene multiplicando la magnitud de ambos vectores y el seno del ángulo entre ellos. Esto significa que un ángulo más grande entre los vectores conducirá a una mayor magnitud del producto cruz. <img alt="Equation 1" src="/files/ftp_upload/14251/14251_Equation_1v3.svg" style="text-align: center; height: 11px;"> La dirección del vector resultante se determina utilizando la regla de la mano derecha. Si rizamos los dedos de la mano derecha desde el vector A hasta el vector B, entonces la dirección del pulgar representa la dirección del vector resultante. En otras palabras, la dirección del producto cruz es perpendicular al plano que contiene los vectores A y B. Es importante tener en cuenta que el producto cruz de vectores no es conmutativo. Es decir, el vector resultante del producto cruz del vector A con el vector B es igual en magnitud, pero opuesto en dirección al producto cruz del vector B con el vector A. Sin embargo, el producto cruz cumple con la ley asociativa y las leyes distributivas de la suma. Esto significa que el producto cruz de una suma de vectores es igual a la suma de los productos cruz de cada vector. En conclusión, el producto cruz es un concepto fundamental en álgebra vectorial que tiene amplias aplicaciones en física e ingeniería, como el cálculo del momento de una fuerza sobre un punto, el cálculo del torque de una fuerza sobre un eje y el cálculo del momento angular de un cuerpo sobre un eje.

Producto Cruz

El producto cruzado es un concepto fundamental en álgebra vectorial que es una operación vectorial sobre dos vectores diferentes para obtener un tercer vector. A diferencia de la ...

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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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