Statement 1: If →A=2^i+3^j+6^k,→B=^i+^j−2^k and →C=^i+2^j+^k, then |→A×(→A×(→A×→B))⋅→C|=243
Statement 2: |→A×(→A×(→A×→B))⋅→C|=|→A|2|[→A→B→C]|
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×((→A⋅→B)→A−(→A⋅→A)→B)⋅→C ={→A×(→A⋅→B)→A−(→A⋅→A)→A×→B}→C =−|→A|2[→A→B→C]
Now, |→A|2=4+9+36=49 [→A→B→C]=∣∣
∣∣23611−2121∣∣
∣∣ =2(1+4)−1(3−12)+1(−6−6) =7