First of all, let me tell you about the cross product of vectors, that is, cross product: cross product, also called outer product and cross product in mathematics, and vector product and cross product in physics, which is a binary operation of vectors in vector space. Unlike dot product, its operation result is vector instead of scalar. The cross product of two vectors is perpendicular to the sum of two vectors.

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.