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|(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2...

`|(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2))|=`

A

`(a-b)(b-c)(c-a)`

B

`-(a-b)(b-c)(c-a)(a+b+c)`

C

`abc(a-b)(b-c)(c-a)`

D

`2(a-b)(b -c)(c-a)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

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

    A
    `(a-b)(b-c)(c-a)`
    B
    `(a-b)(b-c)(c-a)(a+b+c)`
    C
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    D
    `(a-b)(b-c)(c-a)(ab+bc+ca)`

  • If Delta=|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=k(a-b)(b-c)(c-a) then k=

    A
    abc
    B
    0
    C
    1
    D
    -1

  • |(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

    A
    `(a-b)(b-c)(c-a)`
    B
    `(a-b)(b-c)(c-a)(a+b+c)`
    C
    `(a-b)(b-c)(c-a)abc`
    D
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