The direction cosines of z-axis are :

The correct answer is Option (3) → 0, 0, 1

z axis is represented by a point on it as

$\vec v=0\hat i+0\hat j+z\hat k$

$|\vec v|=|z|=z$

so D.C. = $\frac{0}{z},\frac{0}{z},\frac{z}{z}=0,0,1$