If →a,→b,→c are non coplanar vectors such that →b×→c=→a,→a×→b=→c and →c×→a=→b, then
A
∣∣→a∣∣=1
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B
∣∣∣→b∣∣∣=1
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C
∣∣→a∣∣+∣∣∣→b∣∣∣+∣∣→c∣∣=3
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D
None of these
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Solution
The correct options are A∣∣→a∣∣=1 B∣∣∣→b∣∣∣=1 C∣∣→a∣∣+∣∣∣→b∣∣∣+∣∣→c∣∣=3 →c×→a=→b and →a=→b×→c ⇒→c×(→b×→c)=→b ⇒c2→b−(→c.→b)→c=→b ⇒∣∣→c∣∣=1 and →c⋅→b=0 Similarly we can get that ∣∣→a∣∣=∣∣∣→b∣∣∣=1