3D points challenge

Geometry Level 3

The points $$A$$, $$B$$, $$P$$, and $$Q$$ all lie on one line, with $$A=(-3, 5, 8).$$

Point $$P$$ lies in the $$xy$$-plane between $$A$$ and $$B$$ such that the distance from $$A$$ to $$P$$ is twice the distance from $$P$$ to $$B$$. Furthermore, $$Q$$ sits on the $$z$$-axis such that the distance from $$A$$ to $$Q$$ is twice the distance from $$Q$$ to $$B$$.

If $$B=(x,y,z),$$ what is the value of $$x+y+z?$$

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