The angle between vector $$\vec{Q}$$ and the resultant of $$(2\vec{Q} + 2\vec{P})$$ and $$(2\vec{Q} - 2\vec{P})$$ is :

We need to find the angle between $$\vec{Q}$$ and the resultant of $$(2\vec{Q} + 2\vec{P})$$ and $$(2\vec{Q} - 2\vec{P})$$.

Find the resultant.

$$ \vec{R} = (2\vec{Q} + 2\vec{P}) + (2\vec{Q} - 2\vec{P}) = 4\vec{Q} $$

The resultant is $$4\vec{Q}$$, which is in the same direction as $$\vec{Q}$$.

Therefore, the angle between $$\vec{Q}$$ and $$\vec{R} = 4\vec{Q}$$ is $$0°$$.

The correct answer is Option (2): $$0°$$.