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 a = i- 2j + k, b = 2i + j - k, c = 4i + 4j + 3k then |(a xx b) xx c| =

If a = 3i - 2j + k, b = 2i - 4j - 3k, c = -i + 2j + 2k then a + b + c =

If a = 2i + j - 3k, b = I - 2j + k, c -I + j - 4k, d = I + j + k then (a xx b) xx (c xx d) =

Find the real value of a for which 3i^(3)-2ai^(2)+(1-a)i+5 is real

Let a_i^2+b_i^2+c_i^2=1 (for i=1,2,3) and a_ia_j+b_ib_j+c_ic_j=0 (i != j;i,j=1,2,3). Then the absolute value of determinant |(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)| (A) 1/2 (B) 0 (C) 1 (D) 2

If a = I + 2j + 3k, b = -I + 2j + k, c = 3i + j and d is normal to both a and b, then (c,d) =

Let s_1 = {(i,j, k) ∶ i,j, k ∈ {1,2, … ,10}} , s_2 = {(i,j) ∶ 1 ≤ i s_3 = {(i,j, k, l) ∶ 1 ≤ i s_4 = {(i,j, k, l) ∶ i,j, k and l are distinct elements in {1,2, … ,10}} . If the total number of elements in the set s_r is n_r , r= 1,2,3,4, then which of the following statements is (are) TRUE ?

If a.i = 4 then (a . j) xx (2j - 3k) =