Subtraction of vectors can be defined in terms of addition of vectors.

We define the difference of two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ as the sum of two vectors $\overrightarrow{\mathrm{A}}$ and $-\overrightarrow{\mathrm{B}}$.

$\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{A}}+(-\overrightarrow{\mathrm{B}})$

Thus, substraction of vectors means adding opposite of a vector in another vector.

In figure (a), $\vec{A}, \vec{B}$ and $-\vec{B}$ is represented.

In figure (b), $-\vec{B}$ is added to $\vec{A}$.

By triangle method for vector addition,

$\overrightarrow{\mathrm{R}_{2}}=\overrightarrow{\mathrm{A}}+(-\overrightarrow{\mathrm{B}})$

$\therefore\overrightarrow{\mathrm{R}_{2}}=\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}$

(For comparison, $\overrightarrow{\mathrm{R}_{1}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ is shown).