A particle starts from the point P(6,−2,0) and moves to the point Q(−1,4,7). It then moves to a point R such that the vector QR equals twice the vector PQ.
a. (i) Find the displacement vector of the particle for the motion from P to Q.
b. (ii) Determine the coordinates of the point R.
c. (iii) Calculate the magnitude of the direct displacement vector PR.