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Question

Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a makes with vectors b and c respectively and a×(b×c)=12b, then |αβ| is equal to :

A
60
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B
45
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C
30
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D
90
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Solution

The correct option is C 30
a×(b×c)=12b
(ac)b(ab)c=12b
(ac12)b(ab)c=0

As vectors b and c are non-parallel,
ac12=0
ac=12cosβ=12
​​​​​​​ β=60
and ​​​​​​​ab=0 α=90
​​​​​​​|αβ|=30

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