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Question

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
[ABC]
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C
2[ABC]
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D
[ABC]
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Solution

The correct option is D [ABC]
(A+B+C).[(A+B)×(A+C)]
=(A+B+C).[A×C+B×A+B×C]
=A(B×C)+B(A×C)+C(B×A)
=[ABC][ABC][ABC]=[ABC]

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