If $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$are any two vectors and k and m be any scalars, then which of the following is correct?

The addition of vectors and the multiplication of a vector by a scalar together give the following distributive laws.
Let $\overrightarrow{\mathrm{a}}$and $\overrightarrow{\mathrm{b}}$ be any two vectors and k and m be any scalars

then 
$$\begin{gathered} \left(\mathrm{i}\right) \mathrm{k}\overrightarrow{\mathrm{a}}+\mathrm{m}\overrightarrow{\mathrm{a}}=(\mathrm{k}+\mathrm{m})\overrightarrow{\mathrm{a}} \\ \left(\mathrm{ii}\right) \mathrm{k}\left(\mathrm{m}\overrightarrow{\mathrm{a}}\right)=\left(\mathrm{km}\right)\overrightarrow{\mathrm{a}} \\ \left(\mathrm{iii}\right) \mathrm{k}(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}})=\mathrm{k}\overrightarrow{\mathrm{a}}+\mathrm{k}\overrightarrow{\mathrm{b}} \end{gathered}$$