Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are

Question

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are .

Philoid · Accepted Answer

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.

Because,

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

.