The points A(2,−1,3) and B(5,4,−2) are fixed. A variable point R divides the segment AB internally in the ratio t:1, where t>0.
a. (i) Express the coordinates of R in terms of t.
b. (ii) If R lies on the plane x+2y+z=7, find the value of t.
c. (iii) Using the value of t obtained in part (ii), calculate the length AR.