11, Show that the direction cosines ofa vector equally inclined to the axes OX,0Y and 0Z are `1/sqrt3,1/sqrt3,1/sqrt3`

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)`.