3D points challenge

Geometry Level 3

The points AA, BB, PP, and QQ all lie on one line, with A=(3,5,8).A=(-3, 5, 8).

Point PP lies in the xyxy-plane between AA and BB such that the distance from AA to PP is twice the distance from PP to BB. Furthermore, QQ sits on the zz-axis such that the distance from AA to QQ is twice the distance from QQ to BB.

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

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