direction cosines

If the non-zero vector  r=xi+yj+zk  of 3 forms the angles α, β and γ with the positive directions of x-axis, y-axis and z-axis, respectively, then the numbers


are the direction cosinesMathworldPlanetmath of the vector. Any triple l,m,n of numbers, which are proportional ( to the direction cosines, are direction numbers of the vector.

If  r=x2+y2+z2  is the of r, we see easily that


Conversely, the componentsPlanetmathPlanetmath of the vector on the coordinate axes may be obtained from


We also see that the direction cosines satisfy

Title direction cosines
Canonical name DirectionCosines
Date of creation 2013-03-22 17:16:32
Last modified on 2013-03-22 17:16:32
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Definition
Classification msc 15A72
Classification msc 51N20
Related topic MutualPositionsOfVectors
Related topic EquationOfPlane
Defines direction numbers