If A,B and c are three non-coplanar vectors, then (A+B+C).[(A+B)×(A+C)] equals
A
0
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B
[A,B,C]
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C
2[A,B,C]
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D
−[A,B,C]
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Solution
The correct option is B−[A,B,C] (A+B+C).[(A+B)×(A+C)]=(A+B+C).(B×A+A×C+B×C)=(A+B+C).(B×A)+(A+B+C).(A×C)+(A+B+C).(B×C)=C.(B×A)+B.(A×C)+A.(B×C)=−[A,B,C]−[A,B,C]+[A,B,C]=−[A,B,C]