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

Iloczyn krzyżowy to iloczyn dwóch różnych wektorów, którego wypadkową jest trzeci wektor.
Wielkość iloczynu krzyżowego uzyskuje się przez pomnożenie wielkości zarówno wektorów, jak i sinusa kąta między nimi.
W tym miejscu wielkość iloczynu krzyżowego można pomnożyć przez wektor jednostkowy, który określa kierunek wektora wynikowego.
Reguła prawej ręki określa kierunek wektora wynikowego. Jeśli zgięte palce reprezentują kierunek od wektora A do wektora B, to kierunek kciuka reprezentuje kierunek wektora wynikowego.
Wektor wynikowy jest zawsze prostopadły do płaszczyzny zawierającej wektory A i B.
Iloczyn krzyżowy wektorów jest nieprzemienny. Wypadkowa iloczynu krzyżowego wektora A z wektorem B jest równa wielkości, ale przeciwna w kierunku do iloczynu krzyżowego wektora B z wektorem A.
Jednak iloczyn wektorowy podlega prawom asocjacyjnym i dystrybucyjnym.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. str. 125 \u2012 126.</li>
</ol>

iloczyn wektorowy

Cross Product

Iloczyn wektorowy to podstawowe pojęcie w algebrze wektorowej, polegające na wykonaniu operacji wektorowej na dwóch różnych wektorach w celu uzyskania trzeciego. W odróżnieniu od iloczynu skalarnego, iloczyn wektorowy generuje wektor prostopadły do obu wektorów pierwotnych.

Wartość iloczynu wektorowego jest uzyskiwana przez pomnożenie wartości obu wektorów i kąta sinus między nimi. Oznacza to, że większy kąt między wektorami prowadzi do większej wartości iloczynu wektorowego.

<img alt="Equation 1" src="/files/ftp_upload/14251/14251_Equation_1v3.svg" style="text-align: center; height: 11px;" />

Kierunek wektora wynikowego jest określany przy użyciu reguły prawej ręki. Jeśli zaciśniemy palce prawej ręki od wektora A do wektora B, to kierunek kciuka będzie reprezentował kierunek wektora wynikowego. Innymi słowy, kierunek iloczynu wektorowego jest prostopadły do płaszczyzny zawierającej wektory A i B.

Ważne jest, że iloczyn wektorowy jest niekomutatywny. Oznacza to, że wektor wynikowy iloczynu wektorowego wektora strong>A z wektorem B jest równy pod względem wartości, ale przeciwny pod względem kierunku do iloczynu wektorowego wektora B z wektorem A. Jednak iloczyn wektorowy podlega prawu łączności i prawom rozdzielności dodawania. Oznacza to, że iloczyn wektorowy sumy wektorów jest równy sumie iloczynów wektorowych każdego z tych wektorów.

Podsumowując, iloczyn wektorowy to podstawowe pojęcie w algebrze wektorowej, które ma szerokie zastosowanie w fizyce i inżynierii, takie jak obliczanie momentu siły względem punktu, obliczanie momentu siły względem osi oraz obliczanie pędu kątowego ciała względem osi.

Iloczyn wektorowy

Iloczyn wektorowy to podstawowe pojęcie w algebrze wektorowej, które jest operacją wektorową na dwóch różnych wektorach w celu uzyskania trzeciego wektora. W przeciwieństwie do ...

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KEY TERMS AND CONCEPTS

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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.

Cross Product Direction and Magnitude | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Cross Product Direction and Magnitude

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