Suppose we have a vector
in 2-dimensional space, and we would like to find the component of vector
in the direction of horizontal and vertical axis. Using trigonometry we can find the magnitude of vector component to be
. The direction of these vector components are the standard
of horizontal and vertical axes
We can find vector projection of a vector
onto other vector
based on the inner product of the two vectors. Scalar projection of vector
is the magnitude of projection given as
. Vector projection of vector
of projection times the
. Geometrically, vector projection is shown in the figure below.
Projection of vector onto horizontal axis is equivalent to projection of vector onto unit standard vector . The scalar projection is . The projection vector becomes . Cosine angle between two vectors is . Thus, .