For every real number t, define the points
P(t,2t−1,3t+2),
Q(t+1,2t+1,3t+5) and
R(t−2,2t−5,3t−4).
(i) Prove that the points P, Q and R are collinear for all real t.
(ii) Obtain the vector equation of the line that contains these points.
(iii) When t=2, find the ratio in which Q divides the line segment PR. State whether the division is internal or external.
a. Prove that P, Q and R are collinear for every real t.
b. Find the vector equation of the straight line containing the three points.
c. For t=2, determine the ratio in which Q divides PR, specifying the nature of the division.