If `G_1` is the mean centre of `A_1,B_1,C_1 and G_2` that of `A_2,B_2,C_2` then show thast `vec(A_1A_2)+vec(B_1B_2)+vec(C_1C_2)=3vec(G_1G_2)`

If G is the centroid of Delta ABC and G' is the centroid of Delta A' B' C' " then " vec(A A)' + vec(B B)' + vec(C C)' =

If A_1A_2....A_n is a regular polygon. Then the vector vec(A_1A_2)+vec(A_2A_3)+.....vec(A_nA_1) is

Let vec r_1, vec r_2, vec r_3, , vec r_n be the position vectors of points P_1,P_2, P_3 ,P_n relative to the origin Odot If the vector equation a_1 vec r_1+a_2 vec r_2++a_n vec r_n=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a. a_1+a_2+dot+a_n=n b. a_1+a_2+dot+a_n=1 c. a_1+a_2+dot+a_n=0 d. a_1=a_2=a_3dot+a_n=0

If A_1,A_2 be two A.M.\'s G_1,G_2 be the two G.M.\'s and H_1,H_2 be the two H.M.\'s between a and b then (A) (A_1+A_2)/(G_1 G_2)=(a+b)/(ab) (B) (H_1+H_2)/(H_1 H_2)=(a+b)/ab (C) (G_1G_2)/(H_1 H_2)=(A_1+A_2)/(H_1+H_2) (D) (A_1+A_2)/(H_1 H_2)=(a+b)/(a-b)

If Delta=|[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]| and A_1,B_1,C_1 denote the co-factors of a_1, b_1, c_1 respectively, then the value of the determinant |[A_1,B_1,C_1],[A_2,B_2,C_2],[A_3,B_3,C_3]| is-

Let G be the centroid of ABC .If vec AB=vec a,vec AC=vec b ,then the bisector vec AG, in terms of vec a and vec b is (2)/(3)(vec a+vec b) b.(1)/(6)(vec a+vec b) c.(1)/(3)(vec a+vec b) d.(1)/(2)(vec a+vec b)1

If Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| and A_2,B_2,C_2 are respectively cofactors of a_2,b_2,c_2 then a_1A_2+b_1B_2+c_1C_2 is

If vec a,vec b and vec c are any three non-coplanar vectors,then prove that points l_(1)vec a+m_(1)vec b+n_(1)vec c,l_(2)vec a+m_(2)vec b+n_(2)vec c,l_(3)vec a+m_(3)vec b+n_(3)vec c,l_(4)vec a+m_(4)vec b+n_(4)vec c are coplanar if [[n_(1),n_(2),n_(3),n_(4)1,1,1,1]]=0

The vectors vec(AB)=vec(c), vec(BC)=vec(a), vec(CA)=vec(b) , are the sides of a triangles ABC. Which of the following vectors represent (s) the median vec(AD) ? 1. (1)/(2) vec(a)+vec(c) 2. -(1)/(2)vec(b)+(1)/(2)vec(c) 3. vec(1)/(2) vec(a)+vec(b) Select the correct answer using the code given below

A straight line L cuts the lines A B ,A Ca n dA D of a parallelogram A B C D at points B_1, C_1a n dD_1, respectively. If ( vec A B)_1,lambda_1 vec A B ,( vec A D)_1=lambda_2 vec A Da n d( vec A C)_1=lambda_3 vec A C , then prove that 1/(lambda_3)=1/(lambda_1)+1/(lambda_2) .