1) How many line segments can be determined by:-

(i) three collinear points? (ii) three non-collinear points?

2) How many planes can be determined by:-

(i) three collinear points? (ii) three non-collinear points?

if the points are collinear then only 1 line can pass through 3 points 

as colinear mean the points which are on same line

b) If the lines are non collinear 

if line should be pass through all three points then answer is none because non collinear means the points which not lie in a line

if it must contain only two points then number of line will be three ..because we can draw a triangle