Find the value of: `|[1 a^2 a^3],[1 b^2 b^3],[1 c^2 c^3]|`

Find the value of |[3,1,2],[a,b,c],[a^(2),b^(2),c^(2)]| .

Find the value of x if 2^(x-3)=1 (a) 1 (b) 2 (c) 3 (d) 4

If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3)|=0 and the vectors A-=(1, a , a^2), B-=(1, b , b^2), C-=(1, c , c^2) are non-coplanar then the value of abc equal to

If a + b + c = 2, 1/a+1/b+1/c=0, ac=4/b and a^3+b^3+c^3=28 , find the value of a^2+b^2+c^2 . यदि a + b + c = 2, 1/a+1/b+1/c=0, ac=4/b तथा a^3+b^3+c^3=28 है, तो a^2+b^2+c^2 का मान ज्ञात कीजि ए।

If A_1,B_1,C_1, , are respectively, the cofactors of the elements a_1, b_1c_1, , of the determinant "Delta"=|a_1b_1c_1a_1b_2c_2a_3b_3c_3|,"Delta"!=0 , then the value of |B_2C_2B_3C_3| is equal to a1 2 b. a_1 c.a_1^2 d. a1 2^2

If a^2+b^2+c^2+ab+bc+ca<=0 AA a, b, c in R then find the value of the determinant |[(a+b+2)^2, a^2+b^2, 1] , [1, (b+c+2)^2, b^2+c^2] , [c^2+a^2, 1, (c+a+2)^2]| : (A) abc(a^2 + b^2 +c^2) (B) 0 (C) a^3+b^3+c^3 + 3abc (D) 65