Addition of Vectors if their tails don't coincide

Question

To add two vectors do their tails have to coincide ? What if their tails don't coincide as shown in the diagram below ?

Answer 1

For addition, we can move (free) vectors such that tails coincide and apply the ordinary rules.

In that case we have that

$$\vec v_1+\Delta \vec v=\vec v_2 \implies \Delta \vec v=\vec v_2-\vec v_1$$