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Question

If a,b,c are three unit vectors, each is inclined at an angle π3 with the other, then scalar triple product [abc] equals

A
12
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B
12
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C
13
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D
14
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Solution

The correct option is B 12
Given a,b,c are unit vectors
|a|=|b|=|c|=1
Now, a.b=|a||b|cosπ3
a.b=12
Hence, option 'B' is correct.
a.b=b.c=c.a=12
Now, a.a=|a|2=1
So, a.a=b.b=c.c=1
[abc][abc]=∣ ∣ ∣a.aa.ba.cb.ab.bb.cc.ac.bc.c∣ ∣ ∣=∣ ∣ ∣ ∣ ∣ ∣112121211212121∣ ∣ ∣ ∣ ∣ ∣=12
[abc]=12

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