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

Çapraz çarpım, sonucu üçüncü bir vektör olan iki farklı vektörün çarpımıdır.
Çapraz çarpımın büyüklüğü, her iki vektörün büyüklüğü ile aralarındaki açının sinüsü ile çarpılarak elde edilir.
Burada, çapraz çarpımın büyüklüğü, ortaya çıkan vektörün yönünü belirten bir birim vektör ile çarpılabilir.
Sağ el kuralı, elde edilen vektörün yönünü verir. Kıvrılmış parmaklar A vektöründen B vektörüne olan yönü temsil ediyorsa, başparmağın yönü de ortaya çıkan vektörün yönünü temsil eder.
Ortaya çıkan vektör her zaman A ve B vektörlerini içeren düzleme diktir.
Vektörlerin çapraz çarpımı değişmeli değildir. A vektörünün B vektörü ile çapraz çarpımının sonucu, büyüklük olarak eşittir, ancak B vektörünün A vektörü ile çapraz çarpımının yönüne zıttır.
Bununla birlikte, çapraz ürün, ilişkisel ve dağıtıcı yasalara uyar.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu. sayfa 125 \u2012 126.</li>
</ol>

vektör Çarpımı

Cross Product

Vektör cebirinde temel bir kavram olan vektör çarpımı, iki farklı vektör üzerinde yapılan bir vektör işlemidir ve üçüncü bir vektör elde etmek için kullanılır. Skaler çarpımın aksine, vektör çarpımı orijinal vektörlerin her ikisine de dik bir vektör miktarıyla sonuçlanır.

Vektör çarpımının büyüklüğü, vektörlerin büyüklüğünün ve aralarındaki açının sinüsünün çarpımıyla elde edilir. Bu, vektörler arasındaki açının daha büyük olması durumunda vektör çarpımının daha büyük bir büyüklüğe sahip olacağı anlamına gelir.

<img alt="Equation 1" src="/files/ftp_upload/14251/14251_Equation_1v3.svg" style="text-align: center; height: 11px;" />

Sonuç vektörün yönü, sağ el kuralı kullanılarak belirlenir. Sağ elin parmaklarını vektör A'dan vektör B'ye kıvırırsak, başparmak yönü sonuç vektörün yönünü temsil eder. Başka bir deyişle, vektör çarpımının yönü, vektörler A ve B'yi içeren düzlemle dik açı yapar.

Vektörlerin çarpımının komütatif olmadığı önemli bir noktadır. Yani, vektör A'nın vektör B ile çarpımının sonucu, büyüklük olarak aynı ancak yön olarak vektör B'nin vektör A ile çarpımının tersidir. Bununla birlikte, vektör çarpımı toplama yasası ve dağılma yasalarına uyulur. Bu, vektörlerin toplamının vektörlerin çarpımlarının toplamına eşit olduğu anlamına gelir.

Sonuç olarak, vektör cebirinde temel bir kavram olan vektör çarpımı, fizik ve mühendislik gibi birçok alanda yaygın olarak kullanılan uygulamaları vardır. Bir noktanın etrafındaki bir kuvvetin anlık momentini hesaplama, bir eksene göre bir kuvvetin torkunu hesaplama ve bir cismin bir eksene göre açısal momentumunu hesaplama gibi.

Vektör Çarpımı

Çapraz çarpım, vektör cebirinde temel bir kavramdır, yani üçüncü bir vektör elde etmek için iki farklı vektör üzerinde bir vektör işlemidir. Aksine ...

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Force Vectors

Kuvvet Vektörleri

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Cross Product Direction and Magnitude

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