Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are
let the vector equally inclined to OX, OY and OZ at angle α.
Then the direction cosine of the vectors are cos α, cos α and cos α.
Cos2α + Cos2α + Cos2α = 1
⇒ 3 Cos2α = 1
⇒ Cos2α = 1/3
Hence, the direction cosines of the vector which are equally inclined to the axis are