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

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 |.

Let the unit vector E be the direction vector of the straight line M, the vector AB=a, the projection A' of point A on the straight line M and the projection B' of point B on the straight line M, then the vector A'B'? It is called the orthogonal projection of AB on the straight line M or in the direction of vector E, which is called projection for short.

geometry

From the perspective of junior high school mathematics, generally speaking, when an object is irradiated with light, the shadow is obtained on a certain plane (ground, wall, etc.). ) is called the projection of an object, the irradiated light is called the projection line, and the plane where the projection is located is called the projection plane.

Sometimes time is a set of parallel lights, such as sunlight or searchlights. The projection formed by parallel rays is a parallel projection. The projection formed by the same point (light from a point light source) is called central projection. The projection produced by the projection line perpendicular to the projection plane is called orthographic projection. The projection that the projection line is not perpendicular to the projection plane is called oblique projection. The shape and size of the object projection are related to its position and angle relative to the projection plane.

Above content reference: Baidu Encyclopedia-Projection