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Question

Statement 1: If A=2^i+3^j+6^k, B=^i+^j2^k and C=^i+2^j+^k, then |A×(A×(A×B))C|=243

Statement 2: |A×(A×(A×B))C|=|A|2|[ABC]|

A
Both the statements are true and statement 2 is the correct explanation for Statement 1
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B
Both the statements are true but Statement 2 is not the correct explanation for Statement 1
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C
Statement 1 is false and Statement 2 is true
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D
Statement 1 is false and Statement 2 is false
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Solution

The correct option is C Statement 1 is false and Statement 2 is true
A×((AB)A(AA)B)C
={A×(AB)A(AA)A×B}C
=|A|2[ABC]
Now, |A|2=4+9+36=49
[ABC]=∣ ∣236112121∣ ∣
=2(1+4)1(312)+1(66)
=7

||A|2[ABC]|=49×7=343

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