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.

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

Given three vectors vec a , vec b ,a n d vec c two of which are non-collinear. Further if ( vec a+ vec b) is collinear with vec c ,( vec b+ vec c) is collinear with vec a ,| vec a|=| vec b|=| vec c|=sqrt(2)dot Find the value of vec a. vec b+ vec b. vec c+ vec c. vec a a. 3 b. -3 c. 0 d. cannot be evaluated

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 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), b(c+a), c(a+b) are in A.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.

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