Show that the direction cosines of a vector equally inclined to the axes `O X ,\ O Y\ a n d\ O Z` are `1/(sqrt(3)),\ 1/(sqrt(3)),1/(sqrt(3))dot`

Explanation

Let `alpha` is the angle of the vector equally inclined to the axes OX, OY and OZ.

Then, direction cosines will be `(cosalpha,cosalpha,cosalpha)`.

We know, sum of squares of direction cosines is always 1.

`cos^2alpha+cos^2alpha+cos^2alpha=1`

`=>3cos^2alpha=1`

`=>cosalpha = 1/sqrt3`

So, direction cosines are `(1/sqrt3,1/sqrt3,1/sqrt3)`.