Prove that (a,b+c), (b,a+c) and (c,a+b) are collinear.

Show that the points (a,b+c),(b,c+a) and (c,a+b) are collinear.

Using determinant : Show that the points (a,b+c),(b,c+a) and (c,a+b) are collinear .

If a, b, c are in H.P., prove that (a)/(b+c), (b)/(c+a) and (c )/(a+b) are also in H.P.

a,b and c are in A.P. Prove that b+c , c+a and a+b are in A.P.

If a, b, c are in H.P., prove that, a(b+c), b(c+a), c(a+b) are in A.P.

Prove that the points (a,bc-a^(2)),(b,ca-b^(2)),(c,ab-c^(2)) are collinear.

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+(1//a c),c+1//(a b) are also in A.P.

If a, b, c are in H.P., prove that, (a)/(b+c-a), (b)/(c+a-b), (c )/(a+b-c) are in H.P.

If (b-c)^(2), (c-a)^(2), (a-b)^(2) are in A.P. then prove that, (1)/(b-c), (1)/(c-a), (1)/(a-b) are also in A.P.

If omega is an imaginary cube root of unity , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a+b+c)(a+bomega+comega^2)(a+bomega^2+comega)