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Question

A vector R is given by R=A×(B×C). Which of the following is true?

A
R is parallel to A
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B
R must be parallel to B
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C
R must be perpendicular to B
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D
None of the options
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Solution

The correct option is D None of the options
Let A=^i, B=^i+^j, C=^k
R=A×(B×C)=^i×[(^i+^j)×^k]=^i×[^j+^i]=^k
R must be perpendicular to both A and (B×C) according to the given equation, but we got R is neither parallel nor perpendicular to B.

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