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Question

If 2s=a+b+c then ∣ ∣ ∣a2(sa)2(sa)2(sb)2b2(sb)2(sc)2(sc)2c2∣ ∣ ∣ is equal to

A
2s(sa)(sb)(sc)
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B
2s3(sa)(sb)(sc)
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C
2s2(sa)(sb)(sc)
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D
(sa)(sb)(sc)
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Solution

The correct option is B 2s3(sa)(sb)(sc)
∣ ∣ ∣a2(sa)2(sa)2(sb)2b2(sb)2(sc)2(sc)2c2∣ ∣ ∣
C1C1C2,C2C2C3
=∣ ∣ ∣a2(sa)20(sa)2(sb)2b2b2(sb)2(sb)20(sc)2c2c2∣ ∣ ∣
=∣ ∣ ∣s(2as)0(sa)2s(s2b)s(2bs)(sb)20s(s2c)c2∣ ∣ ∣
=s2∣ ∣ ∣(2as)0(sa)2(s2b)(2bs)(sb)20(s2c)c2∣ ∣ ∣

On expanding the above determinant we get,
=2s3(sa)(sb)(sc)

Hence, option 'B' is correct.

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