Suppose that l,m,n are direction cosines of a line "L" If the direction angles of the line are replaced by their supplements, the new direction cosines are

If α,β,γare the angles made by a line ‘L’ with the coordinate axes in the positive direction then direction cosines arel,m,n=cosα,cosβ,cosγIf the direction angles are replaced by their supplements, then the direction cosines are  cosπ−α,cosπ−β,cosπ−γ=−cosα,−cosβ,−cosγ=−l,−m,−n