The scalar projection of a vector on (or onto) a vector, also known as the scalar resolute or scalar component 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 and .
The scalar projection is a scalar, equal to the length of the orthogonal projection of on, with a minus 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 .
Read more about Scalar Projection: Definition Based On Angle θ, Definition in Terms of A and B, Properties
Famous quotes containing the word projection:
“In the case of our main stock of well-worn predicates, I submit that the judgment of projectibility has derived from the habitual projection, rather than the habitual projection from the judgment of projectibility. The reason why only the right predicates happen so luckily to have become well entrenched is just that the well entrenched predicates have thereby become the right ones.”
—Nelson Goodman (b. 1906)