If 0° ≤ θ ≤ 90°, as in this case, the scalar projection of a on b coincides with the length of the vector projection.Vector projection of a on b (a1), and vector rejection of a from b (a2).
In mathematics, the scalar projection of a vector on (or onto) a vector also known as the scalar resolute of in the direction of is given by:
The scalar projection is a scalar, equal to the length of the orthogonal projection of on , with a negative sign if the projection has an opposite direction with respect to .
Multiplying the scalar projection of on by converts it into the above-mentioned orthogonal projection, also called vector projection of on .
^Strang, Gilbert (2016). Introduction to linear algebra (5th ed.). Wellesley: Cambridge press. ISBN978-0-9802327-7-6.