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

Le produit vectoriel est un produit de deux vecteurs différents dont la résultante est un troisième vecteur.
L’intensité du produit vectoriel est obtenue en multipliant l’intensité des deux vecteurs et le sinus de l’angle entre eux.
Ici, l’intensité du produit vectoriel peut être multipliée par un vecteur unitaire qui spécifie la direction du vecteur résultant.
La règle de la main droite donne la direction du vecteur résultant. Si les doigts recourbés représentent la direction du vecteur A au vecteur B, alors la direction du pouce représente la direction du vecteur résultant.
Le vecteur résultant est toujours perpendiculaire au plan contenant les vecteurs A et B.
Le produit vectoriel des vecteurs est non commutatif. La résultante du produit vectoriel du vecteur A avec le vecteur B est égale en norme mais de direction opposée à celle du produit vectoriel B avec le vecteur A.
Cependant, le produit croisé obéit aux lois associatives et distributives.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. pp 125 à 126.</li>
</ol>

produit vectoriel

Cross Product

Le produit vectoriel est un concept fondamental en algèbre vectorielle qui est une opération vectorielle sur deux vecteurs différents pour obtenir un troisième vecteur. Contrairement au produit scalaire, le produit vectoriel donne une quantité vectorielle perpendiculaire aux vecteurs d'origine. La magnitude du produit vectoriel est obtenue en multipliant la magnitude des deux vecteurs et le sinus de l'angle entre eux. Cela signifie qu'un angle plus grand entre les vecteurs entraînera une plus grande magnitude du produit vectoriel. <img alt="Equation 1" src="/files/ftp_upload/14251/14251_Equation_1v3.svg" style="text-align: center; height: 11px;"> La direction du vecteur résultant est déterminée en utilisant la règle de la main droite. Si nous courbons les doigts de la main droite du vecteur A au vecteur B, alors la direction du pouce représente la direction du vecteur résultant. En d'autres termes, la direction du produit vectoriel est perpendiculaire au plan contenant les vecteurs A et B. Il est important de noter que le produit vectoriel des vecteurs n'est pas commutatif. Cela signifie que le vecteur résultant pour le produit vectoriel du vecteur A avec le vecteur B a une magnitude égale mais une direction opposée à celle du produit vectoriel du vecteur B avec le vecteur A. Cependant, le produit vectoriel obéit à la loi associative et aux lois distributives de l'addition. Cela signifie que le produit vectoriel d'une somme de vecteurs est égal à la somme des produits vectoriels de chaque vecteur. En conclusion, le produit vectoriel est un concept fondamental en algèbre vectorielle qui a de nombreuses applications en physique et en génie, telles que le calcul du moment d'une force par rapport à un point, le calcul du couple d'une force autour d'un axe, et le calcul du moment cinétique d'un corps autour d'un axe.

Produit vectoriel

Le produit vectoriel est un concept fondamental en algèbre vectorielle qui est une opération vectorielle sur deux vecteurs différents pour obtenir un troisième vecteur. Contrairement au ...

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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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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...

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Learn how the cross product creates a perpendicular vector, how to use the right-hand rule, and why its size depends on angle, torque, and angular momentum.

Cross Product Direction and Magnitude | JoVE K12

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Cross Product Direction and Magnitude

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