There is also the right-handed rule: if a x b = c, if the coordinate system meets the right-handed rule, when the four fingers of the right hand turn from A to B at a rotation angle not exceeding 180 degrees, the thumb points in the direction of C (? | c | = | a× b | = | a | | b | sin & lta,b & gt? )
The unit vectors I, J and K are three unit vectors satisfying the right-handed rule in the coordinate system, which are equivalent to the I on the X axis, the J on the Y axis and the K on the Z axis. Then according to the right-hand rule i x j, the result is the unit vector k perpendicular to I and J with the length of 1
That would explain it? I x j=k, j x k=i, k x i=j, j x i=-k, k x j =-i, i x k =-j. (For ease of understanding, I suggest you feel the picture with your right hand. )
As for the third-order determinant, if it is expanded, it will be the same as the above formula. This is written for the convenience of memory. When you forget the above formula, you can write this determinant (which is very regular and easy to remember) and expand it yourself.
I don't know. Please ask me again.