Let's use a reference point, or origin, O(0,0,0) for P, Q and T.
If P is the point (2,-3,6), then the vector OP can be written as <2,-3,6>, which is the position vector for P. Similarly, OQ is the position vector for Q=<q1,q2,q3> if Q has the coordinates (q1,q2,q3).
OP+PQ=OQ, so OQ=<2,-3,6>+<2,3,-1>=<4,0,5>. Therefore Q has the coordinates (4,0,5).
Similarly:
OP+PT=OT, so OT=<2,-3,6>+<2,-2,-2>=<4,-5,4> and T has the coordinates (4,-5,4).