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 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 |.

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.

Extended data

Angle between vector A and vector B: When two non-zero vectors are known, vector OA=a and vector OB=b pass through point O, then ∠AOB=θ is called the angle between vectors A and B, and is recorded as

If A and B are not * * * lines, then a×b is a vector with the modulus | a×b | =| A | B | SIN < A, the direction of b & gta×b is perpendicular to A and B, and A, B and A× B form a right-handed system in turn. If a and b*** line, then a×b=0.

If a = (x 1, y 1, 0) and b = (x2, y2, 0), there are:

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