If `sum_(i=1)^n bar a_i=bar 0`, where `|bar a_i=1 AA i`,then the value of `sum_(1 leq i leqj leqn) bar a_i-bar a_j` is

If a_i , i= 1,2,3,4 be four real members of same sign, then the minimum value of sum (a_i/a_j) , i , j in {1,2,3,4} , i != j is : (a) 6 (b) 8 (c) 12 (d) 24

If f(x) =Pi_(i=1)^3(x-a_i) + sum_(i=1)_3 a_i - 3x where a_i < a_(i+1) for i = 1,2, then f(x) = 0 have

If f(x) =Pi_(i=1)^3(x-a_i) + sum_(i=1)_3 a_i - 3x where a_i < a_(i+1) for i = 1,2, then f(x) = 0 have

If b_i=1-a_i ,n a=sum_(i=1)^n a_i ,n b=sum_(i=1)^n b_i ,t h e nsum_(i=1)^n a_i ,b_i+sum_(i=1)^n(a_i-a)^2= a b b. n a b c. (n+1)a b d. n a b

If f(x)= prod_(i=1)^3 (x-a_i) +sum_(i=1)^3a_i-3x where a_i lt a_(i+1) forall i=1,2,. . . then f(x)=0 has

If 2bar(i)-bar(j)+bar(k), bar(i)-3bar(j)-5bar(k), 3bar(i)-4bar(j)-4bar(k) are the vertices of a triangle then the vector equation of the median passing through 2bar(i)-bar(j)+bar(k) is

If bar(X) is the mean of a distribution of X, then under usual notation sum sum_(i=1)^(n)f_(i)(x_(2)-bar(x)) is

Prove that identity : sum_(i=1)^(n) (x_i-bar x)^2 = sum_(i=1)^(n) x_i^2-n bar x^2= sum_(i=1)^(n) x_i^2 -(sum_(i=1)^(n) x_i)^2/n .

A non-zero vector bar(a) , is parallel to the line of intersection of the plane determined by the vectors bar(i), bar(i) + bar(j) and the plane determined by the vectors bar(i)- bar(j), bar(i) + bar(k) Find the angle between bar(a) and the vector bar(i)- 2bar(j) + 2bar(k)

If bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k), bar(c)=bar(i)+bar(k) , then the unit vector in the opposite direction of bar(a)-2bar(b)+3bar(c) is