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)=12→b, then |α−β| 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 C30∘ →a×(→b×→c)=12→b ⇒(→a⋅→c)→b−(→a⋅→b)→c=12→b ⇒(→a⋅→c−12)→b−(→a⋅→b)→c=0
As vectors →b and →c are non-parallel, ∴→a⋅→c−12=0 ⇒→a⋅→c=12⇒cosβ=12 ∴β=60∘ and →a⋅→b=0⇒α=90∘ |α−β|=30∘