a 1b2c 3+b 1c2a 3+c 1a2b 3-a 1c2b 3-b 1a2c 3-c 1b2a 3
A× (b× c) = b (a× c)-c (a× b), so r× (ω× r) = ω r 2-r (ω r).
Lagrange formula: a× (b× c) = b (a c)? C (A) B
The simplified formula and proof of cross multiplication of two-way quantities can be simply written as "BAC-CAB" This formula is very effective for simplifying the vector operation in physics. It should be noted that this formula does not apply to differential operators. Here is a situation related to gradient; This is a special case of Hodge decomposition of Hodge Laplacian operator.
Extended data:
In the spatial rectangular coordinate system, three unit vectors I, J and K in the same direction as the X-axis, Y-axis and Z-axis are taken as a set of bases. If it is an arbitrary vector in the coordinate system, take the coordinate origin o as the starting point to make vector a.
According to the basic theorem of space, there is only one set of real numbers (x, y, z), which makes a=ix+jy+kz. Therefore, the pair of real numbers (x, y, z) is called the coordinate of vector A, and is denoted as a=(x, y, z). This is the coordinate representation of vector A, where (x, y, z) is the coordinate of point P, and vector A is called the position vector of point P..
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