The coordinate formula of vector multiplication is: AB = x1x 2+y1y2 = | a || b | cos θ, where θ is the included angle between vectors A and B. In mathematics, vectors refer to quantities with magnitude and direction.

Vectors with the same length and direction are called equal vectors. Vectors A and B are equal, so let's say A = B ... All zero vectors are equal. When the vector is represented by a directed line segment, the starting point can be arbitrarily selected. Any two equal nonzero vectors can be represented by the same directed line segment.

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.