Vector projection "Go"

Given a vector u and V, the projection vector on V is obtained, such as.

Assume that the projection vector of U on V is U ', and the angle of the vector u and V is theta. A vector has two properties, size and direction, we first determine the size of U ' (that is, length, or modulus), from the end of U do v perpendicular, then D is the length of U '. The direction of the U ' and V is the same, and the direction of V is v/|v| the direction of U '. So there are

(1)

Ask for the length of D again.

(2)

The last to seek cos (theta)

(3)

The joint solution equation (1) (2) (3) is obtained

This is the final projection vector.

and the length of this vector, D, is

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The following is the old derivation, also reserved.

Vector projection "Go"