If $$\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}$$, the angle between $$\vec{P}$$ and $$\vec{Q}$$ is $$\theta$$ ($$0° < \theta < 360°$$). The value of $$\theta$$ will be ______ °.

We are given that $$\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}$$.

From the properties of the cross product, we know that $$\vec{Q} \times \vec{P} = -(\vec{P} \times \vec{Q})$$. Substituting this into the given equation: $$\vec{P} \times \vec{Q} = -(\vec{P} \times \vec{Q})$$.

This gives $$2(\vec{P} \times \vec{Q}) = \vec{0}$$, which means $$\vec{P} \times \vec{Q} = \vec{0}$$.

The cross product $$\vec{P} \times \vec{Q} = |\vec{P}||\vec{Q}|\sin\theta \; \hat{n}$$, where $$\theta$$ is the angle between the two vectors. For this to be zero (assuming neither vector is a zero vector), we need $$\sin\theta = 0$$.

In the range $$0° < \theta < 360°$$, $$\sin\theta = 0$$ at $$\theta = 180°$$. (Note: $$\theta = 0°$$ is excluded by the given constraint.)

Therefore, the angle between $$\vec{P}$$ and $$\vec{Q}$$ is $$\theta = 180°$$.