Show that the vector $\hat i + \hat j + \hat k$ is equally inclined to the axes $OX,OY$ and $OZ$.

Let $\vec a = \hat i + \hat j + \hat k$
$\therefore$

Direction-cosines of $\vec a$ are
$< \cfrac{1}{{\sqrt {1 + 1 + 1} }}$ , $\cfrac{1}{{\sqrt {1 + 1 + 1} }},\cfrac{1}{{\sqrt {1 + 1 + 1} }} >$

i.e., $< \cfrac{1}{{\sqrt 3 }},\cfrac{1}{{\sqrt 3 }},\cfrac{1}{{\sqrt 3 }} >$

Hence the given vector is equally inclined to the axes $OX,OY$ and $OZ$.