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Example:Find Direction Cosines

 Post to:   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

α2 + β2 + γ2 = 1

and

(αβγ) 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