英文中有对于第一式有助记口诀BAC-CAB (BACK-CAB，后面的出租车)，但是不容易记住第一式跟第二式的变化，很容易搞混。 观察两个公式，可得到以下三点：

2020年5月26日 · The vector triple product can be simplified by the so-called BAC-CAB rule: A × (B × C) = B(A ⋅ C) − C(A ⋅ B). Notice that. (A × B) × C = − C × (A × B) = − A(B ⋅ C) + B(A ⋅ C) is an entirely different vector (cross-products are not associative).

2022年10月25日 · 许多人为了方便记忆该公式，用BAC-CAB（BACK-CAB，后面的出租车）来表示它，死背不如理解，接下来进行公式推导。 向量三重积得到的结果也是向量，向量有xyz三个分量，我们先分析x分量，假设，则有： x分量相当于将i的余子式提取出来，也就是右下角的那部分，同理，M的各个分量也是如此，则公式表示为： 同理可得y和z分量： 所以，不难得出： 对 而言， 将得到b向量和c向量所在平面的法向量n，n与a叉积所得向量必处于b和c所在平面，则可表 …

几何矢量的连续两个叉乘的化简也叫 BAC-CAB 定理. 要证明这个定理可以将每个叉乘在各个基底上展开（式 11 ）。 由叉乘的坐标定义（式 11 ）证明 式 1 。 这里对连续叉乘的几何意义略 …

The last expression has a vector triple product of the form →X × (→Y × →Z), which can be manipulated with the BAC-CAB rule. Can you take it from there? (2) is simply repeated application of the BAC-CAB rule. Start with the outermost triple vector product. But the RHS can't be right as the last expression is a scalar!

Manipulating vector expressions using Einstein summation notation is far superior to term by term expansion; it is elegant, compact, and easier to follow (once you are familiar with the notation).

BAC-CAB formula Let's prove the formula a £ (b £ c) = b(a ¢ c) ¡ c(a ¢ b): (1) First o®, by linearity in a; b; c it su±ces to prove the formula for a; b; c being unit vectors. Indeed, suppose is true for unit vectors, now suppose that the a; b; c are not unit, but have length a; b; c, respectively.

6 天之前 · The vector triple product identity is also known as the BAC-CAB identity, and can be written in the form Ax (BxC) = B (A·C)-C (A·B) (1) (AxB)xC = -Cx (AxB) (2) = -A (B·C)+B (A·C).

6 天之前 · From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/BAC-CABIdentity.html. The vector triple product identity Ax (BxC)=B (A·C)-C (A·B). This identity …

1.过程 2.几何意义其中标量三重积的几何意义是——平行六面体的体积，分析如下 不要忘了右手螺旋的轮换特性 3.特别注意——矢量分析中的哈密顿算子与哈密顿算子的运算结合时要特别注意哈密顿算子的作用对象，不能…