Prove that the points (a,b), (a'b'), (a-a',b-b') are collinear iff ab' = a'b.

If the points (x,y),(a,0) and (0,b) are collinear, prove that x/a + y/b = 1, ab ne 0

If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

If the lines AB and AC are parallel to a line l, show that the points A,B and C are collinear.

Prove that: {:|(bc,a,1),(ca,b,1),(ab,c,1)| = (a-b)(b-c)(a-c)

Prove that the angle between the st. lines : (a + b)x + (a-b)y = 2ab and (a-b)x+(a+ b) y = 2ab is tan^-1 frac(2ab)(a^2-b^2) .

Show that : (a+b)^2 - 4ab=(a-b)^2 .

If a, b, c are in A.P., prove that : (a(b+c))/(bc), (b(c+a))/ (ca), (c(a+b))/(ab) are also in A.P.

Prove that the equation : (a+b)^2= 4ab sin^2 theta is possible only when a = b.

Prove that: {:|(1,1,1),(a,b,c),(bc,ca,ab)| = (a-b)(b-c)(c-a)

Prove that: {:|(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)