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2024年4月16日发(作者：structured怎么下载)

两个向量的叉乘计算方法

Vector cross product, also known as vector outer product, is the

operation that takes two vectors and produces another vector

perpendicular to both of the original vectors. This operation is

commonly used in physics, engineering, and computer graphics to

calculate moments, torques, and determine the direction of a

perpendicular to a plane. 叉乘也被称为外积，它是一种以两个向量为输

入并生成另一个垂直于前两个向量的向量的运算。这个运算在物理学、工程

学和计算机图形学中常被用来计算力矩、扭矩并确定一个垂直于平面的方向。

To calculate the cross product of two vectors A and B, the resulting

vector is given by the formula A x B = A B sin(θ)n, where A and B are

the magnitudes of vectors A and B, θ is the angle between A and B,

and n is the unit vector perpendicular to the plane defined by A and

B. This formula actually represents the magnitude of the resulting

vector in addition to its direction. 要计算两个向量A和B的叉乘，结果

向量可以由公式A x B = A B sin(θ)n给出，其中A和B是向量A和B的大

小，θ是A和B之间的夹角，n是A和B所在平面的垂直单位向量。这个

公式实际上代表了结果向量的大小以及方向。

In mathematical terms, the magnitude of the cross product of two

vectors A and B can be calculated as A x B = A B sin(θ), where A x B is

the magnitude of the resulting vector. The sine of the angle between

the two vectors determines the magnitude of the resulting vector,

with a larger angle resulting in a larger magnitude. 在数学术语中，两

个向量A和B的叉乘的大小可以计算为A x B = A B sin(θ)，其中A x B是

结果向量的大小。两个向量之间夹角的正弦值决定了结果向量的大小，夹角

越大，结果向量的大小就会更大。

Another way to calculate the cross product of two vectors is to use

the determinant of a 3x3 matrix. Let A = [a1, a2, a3] and B = [b1, b2,

b3] be the two vectors, then the cross product A x B can be

calculated as:

i j k

a1 a2 a3

b1 b2 b3 用一个3x3矩阵的行列式计算两个向量的叉乘也是一种方法。

假设A = [a1, a2, a3]和B = [b1, b2, b3]是两个向量，则A x B可以计算如

下：

i j k

a1 a2 a3

b1 b2 b3

The result of this calculation gives the components of the resulting

vector in the i, j, and k directions. This method is particularly useful

when dealing with vectors in a 3D space and when the magnitudes

and angles between the vectors are known. 这个计算的结果给出了结果

向量在i、j、k方向上的分量。这种方法特别适用于处理三维空间中的向量

以及当向量的大小和夹角已知时。

In physics, the cross product is used to define the torque exerted by

a force on a point, given by the formula τ = r x F, where τ is the

torque, r is the position vector from the point to the line of action of

the force, and F is the force vector. This definition shows how the

cross product is instrumental in understanding the rotational effects

of forces in three-dimensional space. 在物理学中，叉乘被用来定义力对

一个点产生的扭矩，公式为τ = r x F，其中τ是扭矩，r是从点到力作用线

的位置向量，F是力向量。这个定义显示了叉乘在理解力在三维空间中的旋

转效应上是多么重要。


本文标签： 向量 结果 计算 扭矩 垂直于

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