# Vector projection

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Definition. Projection of the vector AB on the axis l is a number equal to the value of the segment A

_{1}B_{1}on axis l, where points A_{1}and B_{1}are projections of points A and B on the axis l (Fig. 1).Fig. 1 |

Definition. The vector projection of a vector a on a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b.

## Vector projection - formula

The vector projection of a on b is the unit vector of b by the scalar projection of a on b:

proj _{b}a = | a · b | b |

|b|^{2} |

The scalar projection of a on b is the magnitude of the vector projection of a on b.

|proj _{b}a| = | a · b |

|b| |