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In the diagram below, the coordinates of points A and B are (1, 6) and (15, 6) respectively. Point N is on OB such that 3ON=2OB. Line OA is produced to L such that OL= 3OA.
(a) Find vector LN
(b) Given that a point M is on LN such that LM:MN=3:4, find the coordinates if M .
(c) If line OM is produced to T such that OM:MT=6:1
(i) Find the position vectors of T
(ii) Show that points L, T and B are collinear.