If the points (a,0),(0,b) and (1,1) are collinear , then show that `(1)/(a)+(1)/(b)=1`.

If the points ( a_1,b_1),(a_2,b_2) and (a_1+a_2,b_1+b_2) are collinear ,show that a_1b_2=a_2b_1 .

If three points (h, 0),(a, b) and (0, k) lie on a line, show that a/h + b/k = 1 .

Show that the points (-2,3,5) ,(1,2,3) and (7,0,-1) are collinear

Show that the points (a,0),(0,b)and (3a,-2b)are collinear.Also find the equation of the line containing them.

Show that the points A(1,2,7),B(2,6,3) and C(3,10,-1) are collinear.

If the points P (a, 1), Q (1, b), R (-2, 11) are collinear and Q be the mid - point of bar(PR) , then find the value of a and b.

If the points (1,1):(0,sec^2theta); and (cos e c^2theta,0) are collinear, then find the value of theta

Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7) are collinear , and find the ratio in which B divides AC.

Show that the points P(-2,3,5) ,Q (1,2,3) and R (7,0,-1) are collinear

Consider the points O(0,0), A(0,1) , and B(1,1) in the x-y plane. Suppose that points C(x,1) and D(1,y) are chosen such that 0ltxlt1 . And such that O,C, and D are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?.