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If |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|...

If `|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=k(a-b)(b-c)(c-a)`, then k is equal to

A

`-2`

B

1

C

2

D

abc

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The correct Answer is:
B
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Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

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Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

([1,1,1a,b,ca^(2),b^(2),c^(2)])=(a-b)(b-c)(c-a)

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

Value of |(1,a,a^2),(1,b,b^2),(1,c,c^2)| is (A) (a-b)(b-c)(c-a) (B) (a^2-b^2)(b^2-c^2)(c^2-a^2) (C) (a-b+c)(b-c+a)(c+a-b) (D) none of these

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