Vector Projection

The vector projection, also called the vector component or vector resolution, of a vector a onto a nonzero vector b is the orthogonal projection of a onto the straight line running parallel to b, and it can be decomposed into a direction, the unit vector along b, and a scalar magnitude called the scalar projection of a onto b. The remaining part of a, called the vector rejection or the vector component of a perpendicular to b, is the orthogonal projection of a onto the plane or hyperplane orthogonal to b, and since the projection and the rejection always sum back to the original vector a, the rejection can be found simply by subtracting the projection from a. The vector projection itself can be computed directly from the dot product of a and b divided by the dot product of b with itself, multiplied by b.