Vector a Vector b = | a |||| b | * cos θ (θ is the included angle between two vectors).

| a | * cos θ is called the projection of vector a on vector B.

| b | * cos θ is called the projection of vector b on vector a.

Tóuyǐng, a mathematical term, refers to the shadow cast by a figure on a surface or a line.

Let the included angle between two non-zero vectors A and B be θ, then | b | cos θ is called the projection or nominal projection of vector B in the direction of vector A.

By introducing the unit vector a(A) of A into the formula, the vector projection of B on A can be defined.

By definition, the projection of one vector in the direction of another vector is a quantity. When θ is an acute angle, it is positive; When θ is a right angle, it is 0; When θ is an obtuse angle, it is negative; When θ = 0, it is equal to | b | When θ = 180, it is equal to | b |.

The formula of vector projection theorem is | a | cos θ = (a b)/| b |, also called Euclid theorem. In a right triangle, the height on the hypotenuse is the median of the projection of two right-angled sides on the hypotenuse, and each right-angled side is the median of the projection of this right-angled side on the hypotenuse and the ratio of the hypotenuse.

In mathematics, vectors (also known as Euclidean vectors, geometric vectors and vectors) refer to quantities with magnitude and direction.

Extended knowledge

Projection theorem is a basic theorem in mathematics, which describes the projection of one vector on another vector in vector space. The formula of projective theorem can be expressed by the inner product of vector and the length of vector.

There is a vector space v and two vectors u and v in it. The projective theorem shows that the projection of vector U on vector union can be calculated by the following formula: proj-v (u) = (u v)/(| v | 2) * v. Where proj_v(u) is the projection of vector U on vector V, indicating the inner product of vector, and v indicating the length of vector V..