Vector computing Vector contains direction and size, but with direction operation does not change the size of it?

It's true that in physics
Vector multiplication is divided into point multiplication and cross multiplication. There are two kinds of vector multiplication, namely inner product and outer product
Inner product is also called scalar product because its result is a number (scalar)
The inner product of vectors a and B is | a | * | B | cos, where is the angle between a and B
The vector outer product is also called cross product. The result is a vector whose direction is perpendicular to the plane | a | * | B | sin where a and B lie according to the right-handed system

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