1, scalar product: it is a binary operation, accepting two vectors on the real number r and returning a real scalar. It is the standard inner product of Euclidean space.

2. Cross product is a binary operation of vectors in vector space.

Second, the geometric meaning is different.

1. scalar product: in the dot product operation, the first vector is projected onto the second vector (the order of the vectors here is not important, and the dot product operation is interchangeable), and then it is "standardized" by dividing by their scalar lengths. In this way, this score must be less than or equal to 1, which can be simply converted into an angle value.

2. Cross product: The length of cross product |a×b| can be interpreted as the area of the parallelogram formed at the beginning of two cross vectors A and b***. Accordingly, the volume of a parallelepiped with sides A, B and C can be obtained by mixing the product [ABC] = (A× B) C.

Third, the application is different.

1, scalar product: the scalar product of plane vector A B is a very important concept, which can be used to easily prove many propositions of plane geometry, such as Pythagorean theorem, diagonal lines of diamonds are perpendicular to each other, diagonal lines of rectangles are in phase, and so on.

2. Cross product: In physical optics and computer graphics, cross product is used to solve the illumination-related problems of objects. The core of solving illumination is to find the normal of the object surface, and the cross product operation ensures that the normal can be found by cross product as long as two non-parallel vectors (or three points not on the same line) on the object surface are known.

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