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|(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=...

`|(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=`

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If bc+ca+ab=18 , and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=lambda|(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))| the value of lambda is

If a , b, c are real numbers such that a-b=1, b-c=3 , then the number of matrices of the form A[(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))] such that |A|=-12 , is

|(1,1,1),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3))|=

Match the following from List - I to List - II {:("List-I","List-II"),((I)|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=,(a)(a-b)(b-c)(c-a)),((II)|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}|=,(b)(a-b)(b-c)(c-a)abc),((III)|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}

If Delta_(1)=|{:(a_(1)^(2)+b_(1)+c_(1),a_(1)a_(2)|b_(2)|c_(2),a_(1)a_(3)+b_(3)+c_(3)),(b_(1)b_(2)+c_(1),b_(2)^(2)+c_(2),b_(2)b_(3)+c_(3)),(c_(1)c_(3),c_(2)c_(3),c_(3)^(2)):}|" and " Delta_(2)=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| , then find the value of (Delta_(1))/(Delta_(2)) .

IF Delta_1=|{:(a_1^2+b_1+c_1,a_1a_2+b_2+c_2,a_1a_3+b_3+c_3),(b_1b_2+c_1,b_2^2+c_2,b_2b_3+c_1),(c_3c_1,c_3c_2,c_3^2):}|,Delta_2|{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}| then find the value of (Delta_1)/(Delta_2)