Question

what is scalar projection

Answer 1

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:



where the operator denotes a dot product, is the unit vector in the direction of  is the length of , and is the angle between  .

The term scalar component refers sometimes to scalar projection, as, in Cartesian coordinates, the components of a vector are the scalar projections in the directions of the coordinate axes.

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 ofon  byconverts it into the above-mentioned orthogonal projection, also called vector projection of