Write two different vectors having same direction.

Consider $\vec{p}=(\hat{i}+\hat{j}+\hat{k})$ and $\vec{q}=(2 \hat{i}+2 \hat{j}+2 \hat{k})$.

The direction cosines of $\vec{p}$ are given by,

$l=\frac{1}{\sqrt{1^{2}+1^{2}+1^{2}}}=\frac{1}{\sqrt{3}}, m=\frac{1}{\sqrt{1^{2}+1^{2}+1^{2}}}=\frac{1}{\sqrt{3}}$, and $n=\frac{1}{\sqrt{1^{2}+1^{2}+1^{2}}}=\frac{1}{\sqrt{3}} .$

The direction cosines of $\vec{q}$ are given by

$l=\frac{2}{\sqrt{2^{2}+2^{2}+2^{2}}}=\frac{2}{2 \sqrt{3}}=\frac{1}{\sqrt{3}}, m=\frac{2}{\sqrt{2^{2}+2^{2}+2^{2}}}=\frac{2}{2 \sqrt{3}}=\frac{1}{\sqrt{3}}$,

and $n=\frac{2}{\sqrt{2^{2}+2^{2}+2^{2}}}=\frac{2}{2 \sqrt{3}}=\frac{1}{\sqrt{3}}$

The direction cosines of $\vec{p}$ and $\vec{q}$ are the same. Hence, the two vectors have the same direction.