Direction cosine
Encyclopedia
In analytic geometry
, the direction cosines of a vector are the cosines of the angles between the vector and the three coordinate axes. Or equivalently it is the component contributions to the unit vector.
If v is a vector
where
is a basis
. Then the direction cosines are
Note that
and is the Cartesian coordinates of the unit vector
More generally, direction cosine refers to the cosine of the angle between any two vectors. They are useful for forming direction cosine matrices that express one set of orthonormal basis vectors in terms of another set, or for expressing a known vector in a different basis.
Analytic geometry
Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties...
, the direction cosines of a vector are the cosines of the angles between the vector and the three coordinate axes. Or equivalently it is the component contributions to the unit vector.
If v is a vector
where
is a basisBasis (linear algebra)
In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system"...
. Then the direction cosines are
Note that
and is the Cartesian coordinates of the unit vector
More generally, direction cosine refers to the cosine of the angle between any two vectors. They are useful for forming direction cosine matrices that express one set of orthonormal basis vectors in terms of another set, or for expressing a known vector in a different basis.