Name: cross product of two vectors
Uploaded: 2023-09-22T11:49:38.000Z
Duration: 1 min 17 s
Channel: JoVE

Il prodotto incrociato o vettoriale di due vettori è il prodotto delle loro grandezze e del seno dell'angolo. È diretto perpendicolarmente al piano dei vettori.
Geometricamente, è l'area del parallelogramma attraversata dai vettori.
Utilizzando la regola della mano destra, se l'indice e il medio della mano destra puntano rispettivamente il primo e il secondo vettore, il pollice punta verso il loro prodotto incrociato.
Il prodotto incrociato del secondo vettore con il primo ha la direzione opposta. Quindi, l'ordine è importante per i prodotti incrociati.
La misura della rotazione di una porta risulta da una coppia che è il prodotto trasversale della distanza radiale tra la cerniera e il punto di applicazione della forza con la forza applicata.
La porta non ruota se una forza agisce lungo o in senso opposto alla direzione della distanza radiale.
Per il vettore unitario di un asse, il suo prodotto incrociato con se stesso è zero. Ma con un altro, è il terzo in ordine ciclico.
Le componenti del prodotto incrociato dei vettori A e B sono AyBz meno AzB y, AzBx meno AxBz e AxBy meno AyBx.

prodotto vettoriale o incrociato

Vector or Cross Product

La moltiplicazione vettoriale di due vettori produce un prodotto vettoriale, avente grandezza uguale al prodotto dei singoli vettori moltiplicati per il seno del loro angolo e la direzione perpendicolare ad entrambi i singoli vettori. Siccome ci sono sempre due direzioni perpendicolari a un dato piano, una su ciascun lato, la direzione del prodotto vettoriale è determinata dalla regola della mano destra.

Consideriamo il prodotto incrociato di due vettori. Immaginiamo di ruotare il primo vettore intorno alla linea perpendicolare finché non è allineato con il secondo, scegliendo l'angolo più piccolo dei due presenti tra i due vettori. Le dita della mano destra sono curvate attorno alla linea perpendicolare in modo che la punta delle dita indichi la direzione di rotazione; il pollice poi punta nella direzione del prodotto incrociato.

Similmente, la direzione di un prodotto incrociato del secondo vettore con il primo viene determinata ruotando il secondo vettore sul primo e risulta essere opposta al prodotto incrociato del primo vettore con il secondo. Questo implica che i due vettori sono tra loro antiparalleli. Il prodotto incrociato di due vettori è anti-commutativo, questo significa che il prodotto vettoriale inverte il segno quando l'ordine di moltiplicazione viene invertito. Il prodotto vettoriale di qualsiasi vettore con se stesso è zero.

Consideriamo alcuni casi in cui viene applicato il prodotto vettoriale. Il vantaggio meccanico che una chiave può fornire dipende dalla grandezza della forza applicata, dalla sua direzione rispetto alla maniglia della chiave e da quanto lontano dal dado viene applicata la forza. La grandezza fisica del vettore che fa girare il dado è chiamata coppia, ed è il prodotto vettoriale della forza applicata al vettore con il vettore di posizione; un altro esempio è il caso di una particella che si muove in un campo magnetico in cui sperimenta una forza magnetica. Il campo magnetico, la forza magnetica e la velocità sono grandezze vettoriali. Il vettore forza è proporzionale al prodotto vettoriale della velocità vettoriale con il vettore del campo magnetico.

Questo testo è stato tratto e adattato da <a href="https://openstax.org/books/university-physics-volume-1/pages/2-4-products-of-vectors">Openstax, University Physics Volume 1, Section 2.4: Products of Vectors.</a>

Prodotto vettoriale o incrociato

La moltiplicazione vettoriale di due vettori produce un prodotto vettoriale, con la grandezza uguale al prodotto dei singoli vettori moltiplicato per il seno di ...

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cross product of two vectors

The cross product of two vectors gives a new vector that is related to both original vectors. It is also called the vector product. In many physics problems, this operation helps describe quantities that depend on direction as well as size.

The result of a cross product has a direction set by the two input vectors. It is not the same as ordinary multiplication. The transcript focuses on the vector or cross product as a core vector operation students use when working with vectors in science.

Cross Product of Two Vectors

introduction to scalers

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vector or cross product

The cross product of two vectors gives a new vector that is related to both original vectors. It is also called the vector product. In many physics problems, this operation helps describe quantities that depend on direction as well as size. The result of a cross product has a direction set by the two input vectors. It is not the same as ordinary multiplication. The transcript focuses on the vector or cross product as a core vector operation students use when working with vectors in science.

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position and displacement vectors

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key terms and concepts

Learn the cross product of two vectors, also called the vector product, and how it creates a new vector with direction in physics and math.

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Cross Product of Two Vectors

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