Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are \[\frac{1}{\sqrt{3}}\],\[\frac{1}{\sqrt{3}}\],\[\frac{1}{\sqrt{3}}\].

Firstly,

Let’s assume a vector to be equally inclined to axes OX, OY, and OZ at angle \[\alpha \].

Then, the direction cosines of the vector are \[\cos \alpha \],\[\cos \alpha \]and \[\cos \alpha \].

Now, we know that

Therefore, the direction cosines of the vector which are equally inclined to the axes are \[\frac{1}{\sqrt{3}}\],\[\frac{1}{\sqrt{3}}\],\[\frac{1}{\sqrt{3}}\].

Hence proved.