If `|[b^2+c^2,a b,a c],[ a b, c^2+a^2,b c],[c a, c b, a^2+b^2]|=k a^2b^2c^2,` then the value of `k` is `a b c` b. `a^2b^2c^2` c. `b c+c a+a b` d. none of these

Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2

If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c +a,a +b,b +c)| = k |(a,b,c),(c,a,b),(b,c,a)| , then the value of k, is 1 b. 2 c. 3 d. 4

Prove that |[a-b-c,2a,2a],[2b, b-c-a, 2b],[2c, 2c, c-a-b]|= (a+b+c)^3 .

If |b+c c+a a+b a+b b+c c+a c+a a+b b+c|=k|ab c c a b b c a| , then value of k is 1 b. 2 c. 3 d. 4

If a ,\ b ,\ &\ c are non zero real numbers, then |b^2c^2bcb+c c^2a^2cac+a a^2b^2aba+b| is equal to a. a^2b^2c^2(a+b+c) b. a b c(a+b+c)^2 c. zero d. none of these

If |(a^2,b^2,c^2),((a+b)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

If |(a^2,b^2,c^2),((a+b)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)