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

Il prodotto incrociato è un prodotto di due vettori diversi la cui risultante è un terzo vettore.
La grandezza del prodotto incrociato si ottiene moltiplicando la grandezza di entrambi i vettori e il seno dell'angolo tra di essi.
Qui, l'entità del prodotto incrociato può essere moltiplicata per un vettore unitario che specifica la direzione del vettore risultante.
La regola della mano destra fornisce la direzione del vettore risultante. Se le dita arricciate rappresentano la direzione dal vettore A al vettore B, la direzione del pollice rappresenta la direzione del vettore risultante.
Il vettore risultante è sempre perpendicolare al piano contenente i vettori A e B.
Il prodotto incrociato dei vettori non è commutativo. La risultante del prodotto incrociato del vettore A con il vettore B è uguale in grandezza ma opposta in direzione a quella del prodotto incrociato del vettore B con il vettore A.
Tuttavia, il prodotto incrociato obbedisce alle leggi associative e distributive.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pp 125 \u2012 126.</li>
</ol>

prodotto vettoriale

Cross Product

Il prodotto vettoriale è un concetto fondamentale nell'algebra vettoriale, questo è un'operazione vettoriale su due vettori diversi per ottenere un terzo vettore. A differenza del prodotto scalare, il prodotto vettoriale produce una quantità vettoriale perpendicolare a entrambi i vettori originali.

La magnitudine del prodotto vettoriale, si ottiene moltiplicando la magnitudine di entrambi i vettori e il seno dell'angolo tra di essi. Ciò significa che un angolo più grande tra i vettori porterà a una maggiore magnitudine del prodotto vettoriale.

<img alt="Equation 1" src="/files/ftp_upload/14251/14251_Equation_1v3.svg" style="text-align: center; height: 11px;" />

La direzione del vettore risultante è determinata utilizzando la regola della mano destra. Se si arricciano le dita della mano destra dal vettore A al vettore B, la direzione del pollice rappresenta la direzione del vettore risultante. In altre parole, la direzione del prodotto vettoriale è perpendicolare al piano che contiene i vettori A e B.

È importante notare che il prodotto vettoriale dei vettori non è commutativo. Cioè, il vettore risultante per il prodotto vettoriale del vettore A con il vettore B ha la stessa magnitudine ma una direzione opposta rispetto al prodotto vettoriale del vettore B con il vettore A. Tuttavia, il prodotto vettoriale rispetta la legge associativa e le leggi distributive dell'addizione. Ciò significa che il prodotto vettoriale di una somma di vettori è uguale alla somma dei prodotti vettoriali di ciascun vettore.

In conclusione, il prodotto vettoriale è un concetto fondamentale nell'algebra vettoriale che ha ampie applicazioni in fisica e ingegneria, come il calcolo del momento di una forza rispetto a un punto, il calcolo della coppia di una forza rispetto a un asse e il calcolo del momento angolare di un corpo rispetto a un asse.

Prodotto vettoriale

Il prodotto incrociato è un concetto fondamentale dell'algebra vettoriale, ovvero un'operazione vettoriale su due vettori diversi per ottenere un terzo vettore. A differenza del ...

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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.

Cross Product Direction and Magnitude

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cross product

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...

key terms and concepts

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.

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Cross Product Direction and Magnitude

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