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If p + q + r = a + b + c = 0, then the d...

If `p + q + r = a + b + c = 0`, then the determinant `|{:(pa,qb,rc),(qc,ra,pb),(rb,pc,qa):}|` equals

A

0

B

`pa+qb+rc`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`|{:(pa,,qb,,rc),(qc,,ra,,pb),(rb,,pc,,qa):}|`
`=pqr(a^(3)+b^(3)+c^(3)-3abc)-(abc(p^(3)+q^(3)+r^(3)-3pqr)`
`=pqr(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)`
`-abc (p+q+r)(p^(2)+q^(2)+r^(2)-pq-qr-pr)`
`=0`
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