Question

Let u and v denote the vectors PQ and PT. u= (2,3-1) v= (2,-2,-2).

Find the coordinates of Q and T, if P has the coordinates (2,-3,6)

Answer 1

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).