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

Das Kreuzprodukt ist ein Produkt aus zwei verschiedenen Vektoren, dessen Resultante ein dritter Vektor ist.
Die Größe des Kreuzprodukts erhält man, indem man die Größe der Vektoren und den Sinus des Winkels zwischen ihnen multipliziert.
Hier kann die Größe des Kreuzprodukts mit einem Einheitsvektor multipliziert werden, der die Richtung des resultierenden Vektors angibt.
Die rechte Regel gibt die Richtung des resultierenden Vektors an. Wenn die gekrümmten Finger die Richtung von Vektor A zu Vektor B darstellen, dann stellt die Richtung des Daumens die Richtung des resultierenden Vektors dar.
Der resultierende Vektor steht immer senkrecht zu der Ebene, die die Vektoren A und B enthält.
Das Kreuzprodukt der Vektoren ist nicht-kommutativ. Die Resultierende des Kreuzprodukts von Vektor A mit Vektor B ist gleich groß, aber entgegengesetzt zu der des Kreuzprodukts von Vektor B mit Vektor A.
Das Kreuzprodukt gehorcht jedoch den assoziativen und distributiven Gesetzen.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. S. 125 \u2012 126.</li>
</ol>

kreuzprodukt

Cross Product

Das Kreuzprodukt ist ein grundlegender Begriff in der Vektoralgebra, der eine Vektoroperation auf zwei verschiedene Vektoren anwendet, um einen dritten Vektor zu erhalten. Im Gegensatz zum Skalarprodukt ergibt das Kreuzprodukt eine vektorielle Größe, die senkrecht zu beiden Ausgangsvektoren steht. Die Größe des Kreuzprodukts wird durch Multiplikation der Größe beider Vektoren und dem Sinus des Winkels zwischen ihnen erhalten. Das bedeutet, dass ein größerer Winkel zwischen den Vektoren zu einer größeren Größe des Kreuzprodukts führt. <img alt="Equation 1" src="/files/ftp_upload/14251/14251_Equation_1v3.svg" style="text-align: center; height: 11px;"> Die Richtung des resultierenden Vektors wird mit der Rechte-Hand-Regel bestimmt. Wenn wir die Finger der rechten Hand von Vektor A zu Vektor B krümmen, dann repräsentiert die Richtung des Daumens die Richtung des resultierenden Vektors. Mit anderen Worten, die Richtung des Kreuzprodukts steht senkrecht zur Ebene, die die Vektoren A und B enthält. Es ist wichtig zu beachten, dass das Kreuzprodukt von Vektoren nicht kommutativ ist. Das bedeutet, dass der resultierende Vektor für das Kreuzprodukt von Vektor A mit Vektor B in der Größe gleich, aber entgegengesetzt zur Richtung des Kreuzprodukts von Vektor B mit Vektor A ist. Das Kreuzprodukt jedoch erfüllt das Assoziativgesetz und die distributiven Gesetze der Addition. Das bedeutet, dass das Kreuzprodukt einer Summe von Vektoren gleich der Summe der Kreuzprodukte jedes Vektors ist. Zusammenfassend ist das Kreuzprodukt ein grundlegender Begriff in der Vektoralgebra mit vielfältigen Anwendungen in Physik und Ingenieurwesen, wie z.B. Berechnung des Drehmoments einer Kraft um einen Punkt, Berechnung des Drehmoments einer Kraft um eine Achse und Berechnung des Drehimpulses eines Körpers um eine Achse.

Kreuzprodukt

Das Kreuzprodukt ist ein grundlegendes Konzept in der Vektoralgebra, das eine Vektoroperation auf zwei verschiedenen Vektoren ist, um einen dritten Vektor zu erhalten. Im Gegensatz zum ...

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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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Cross Product Direction and Magnitude

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