The four fingers of the right hand are combined except the thumb, the thumb is perpendicular to the other four fingers, and the four fingers hold the direction of A vector to the direction of B vector. At this point, the thumb points in the direction of the cross product of the A and B vectors. That is to say, the direction of AB cross product is perpendicular to the plane determined by AB vector. As shown in the figure below:

Cross product, also known as outer product and cross product in mathematics and vector product and cross product in physics, 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. It is also widely used, usually in physical optics and computer graphics.

Extended data

Algebraic rules of cross product

1, anti-commutative law: a× b =-b× a.

2. Distribution law of addition: a× (b+c) = a× b+a× c.

3. compatible scalar multiplication: (ra)×b=a×(rb)=r(a×b).

4. Does not satisfy the associative law, but satisfies Jacobian identity: a×(b×c)+b×(c×a)+c×(a×b)=0.

5. Distribution law, linearity and Jacobian identity show that R3, vector addition and cross product form a Lie algebra respectively.

6. Two nonzero vectors A and B are parallel if and only if a×b=0.

References:

Baidu encyclopedia-cross products