Math M2 Vector in 3D#(20pts)

OP = (3, 8 , -1)
OQ = (9, 7, 2)
So vector = PQ = OQ - OP = (9,7,2) - (3,8, - 1) = (6, -1, 3)
Let PR : RQ = 1 : k
so vector PR = [1/(1 + k)](6, -1, 3).
(a) 1 : 1, that is k = 1
so PR = (1/2)(6,-1,3) = (3, -1/2, 3/2), so co-ordinates of R is (3, -1/2, 3/2)
(b) 2 : 1, that is k = 1/2
so PR = (2/3)(6, -1, 3) = (4, -2/3, 2).
(c) 1 : 2, that is k = 2
so PR = (1/3)(6, -1, 3) = (2, -1/3, 1).