Vector multiplication, also known as cross product and outer product, is a binary operation of vectors in vector space. Different from dot product, its operation result is a pseudo vector instead of a scalar, and the cross product of two vectors is perpendicular to both vectors.

Lagrange formula: a× (b× c) = b (a c)? C (A) B

Extended data:

Algebraic rules

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.