Explanation:
Direction cosine
In analytic geometry, the direction cosines of a vector are the cosines of the angles between the
vector and the three coordinate axes.
If v is a vector
where is a basis. Then the direction
cosines are
(Our solved example in mathguru.com uses
this concept)
Note that
α^{2} + β^{2} +
γ^{2} = 1
and
(α, β, γ) 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 orthonormalbasis vectors in terms of another set, or for
expressing a known vector in a different basis.
http://en.wikipedia.org/wiki/Direction_cosine
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons
Attribution- ShareAlike 3.0 Unported License.
(Our solved example in mathguru.com uses the below concept. This
is our own explanation, it is not taken from Wikipedia.)
For any vector r = a + b+ c its
direction ratios are a : b : c. Its direction cosines are
l = a / (a^{2}
+b^{2} +c^{2})
m = a / (a^{2}
+b^{2} +c^{2})
n = a / (a^{2}
+b^{2} +c^{2})