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Question

If a,b,c be the three non-zero and non-collinar vectors such that a×b=c and b×c=a, then which of the following is/are true

A
a is perpendicular to b
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B
b is perpendicular to c
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C
|b|=1
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D
|b|=2
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Solution

The correct option is C |b|=1
Given a=b×c
a=b×(a×b)
(a×b=c)
a=(bb)a(ba)ba=|b|2a(ba)bComparing both the sides, we get|b|2=1(ba)=0|b|=1 and ab=0a is perpendicular to b

Now, c=a×b=(b×c)×b=(bb)c(cb)bc=|b|2c(cb)bOn comparing both the sides|b|2=1and (cb)=0b is perpendicular to c

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