The geometric meaning of the cross product of the difference between two vectors and the sum of two vectors

The geometric meaning of the cross product of the difference between two vectors and the sum of two vectors

a. B the cross product of the difference between two vectors and the sum of two vectors is still a vector
The geometric meaning is: the four fingers of the right hand bend in the direction of the subtracted vector in the same direction as the subtracted vector, and the direction of the thumb is its direction, which is twice the area of the parallelogram surrounded by the two vectors
(a-b)×(a+b)=a×a+a×b - b×a - b×b
=0+a×b+a×b - 0
=2a×b