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Question

∣ ∣ ∣1aa21bb21cc2∣ ∣ ∣=

A
a2+b2+c2
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B
(a+b) (b+c) (c+a)
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C
(a-b) (b-c) (c-a)
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D
None of these
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Solution

The correct option is C (a-b) (b-c) (c-a)
∣ ∣ ∣1aa21bb21cc2∣ ∣ ∣=∣ ∣ ∣0aba2b20bcb2c21cc2∣ ∣ ∣,byR1R1R2R2R2R3
=(ab)(bc)∣ ∣01a+b01b+c1cc2∣ ∣=(ab)(bc)∣ ∣00ac01b+c1cc2∣ ∣,byR1R1R2=(ab)(bc)(ac)∣ ∣00101b+c1cc2∣ ∣
= (a-b) (b-c) (a-c). (-1) = (a-b) (b-c) (c-a).


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