$\vec{A}$ and $\vec{B}$ are to be added as shown in figure $(a).$

Select a point $\mathrm{O}$ as shown in figure $(b)$.

Represent $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ such that their lengths and directions remain unchanged and their tails remain at $\mathrm{O}$.

Draw a parallelogram $\square^{\mathrm{m}}$ OPSQ in which $\vec{A}$ and $\vec{B}$ are adjacent sides of it. Draw a diagonal OS from $\mathrm{O}$.

Vector $\overrightarrow{\mathrm{OS}}$ represent resultant vector of addition of $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$.

$\overrightarrow{\mathrm{OS}}=\overrightarrow{\mathrm{OP}}+\overrightarrow{\mathrm{OQ}} \quad \therefore \overrightarrow{\mathrm{R}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$

Triangle method for vector addition is shown in figure $(c)$.

If is clear that both methods give equal resultant vector. Hence, both methods are comparable to each other.

Here, magnitude of resultant vector $\overrightarrow{\mathrm{R}},|\overrightarrow{\mathrm{R}}| \leq|\overrightarrow{\mathrm{A}}|+|\overrightarrow{\mathrm{B}}|$