Let a→,b→ and c→ be vectors forming right-hand triad. Let p→=b→×c→[a→b→c→],q→=c→×a→[a→b→c→] and r→=a→×b→[a→b→c→] If x∈R+ then
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a
x[a→b→c→]+[p→q→r→]x has least value 2
b
x4[a→b→c→]2+[p→q→r→]x2 has least value 3/22/3
c
[p→q→r→]>0
d
none of these
answer is A.
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Detailed Solution
we have [p→q→r→]=b→×c→[a→b→c→],c→×a→[a→b→c→],a→×b→[a→b→c→]=b→×c→,c→×a→,a→×b→[a→b→c→]3=[a→b→c→]2[a→b→c→]3=1[a→b→c→].therefore [p→q→r→]>01 x>0,x[a→b→c→]+[p→q→r→]x≥2 (using A.M. > G.M.) (2) Similarly, use A.M.≥ G.M.