The direction cosines of the line that makes equal angles with three axes in a space are
Notice that we verify ± 1/ 3, ±1/ 3, ±1/ 3 by full calculation: use standard identity, substitute, simplify step by step to reach ± 1/ 3, ±1/ 3, ±1/ 3.
Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry
