## Calculus (3rd Edition)

First we add the vectors ${{\bf{v}}_1} + {{\bf{v}}_2}$ and draw the vector. Then we add ${{\bf{v}}_3}$ to this vector, so we get ${{\bf{v}}_1} + {{\bf{v}}_2} + {{\bf{v}}_3}$. Finally, we add ${{\bf{v}}_4}$ to this vector and we get ${\bf{v}} = {{\bf{v}}_1} + {{\bf{v}}_2} + {{\bf{v}}_3} + {{\bf{v}}_4}$.
To sketch the vector sum ${\bf{v}} = {{\bf{v}}_1} + {{\bf{v}}_2} + {{\bf{v}}_3} + {{\bf{v}}_4}$: First we add the vectors ${{\bf{v}}_1} + {{\bf{v}}_2}$ and draw the vector (the dashed vector as is shown in the figure attached). Then we add ${{\bf{v}}_3}$ to this vector, so we get ${{\bf{v}}_1} + {{\bf{v}}_2} + {{\bf{v}}_3}$ (the dashed vector in the figure). Finally, we add ${{\bf{v}}_4}$ to this vector and we get ${\bf{v}} = {{\bf{v}}_1} + {{\bf{v}}_2} + {{\bf{v}}_3} + {{\bf{v}}_4}$ (the red vector in the figure).