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

Question

Philoid · Accepted Answer

Let a vector be equally inclined to axes OX, OY, and OZ at angle

Then, the direction cosines of the vector are l = cosα, m = cosα and n = cos α

And, we know that –

l² + m² + n² = 1

cos²α + cos²α + cos²α = 1

3 cos²α = 1

Hence, the direction cosines of the vector which are equally inclined to the axes are