[JEE Advanced 2013] v a i b j c k a b c in 1 1 8
$V=\{a\hat i+b\hat j+c\hat k:a,b,c\in\{-1,1\}\}$ ($8$ vectors). Three non-coplanar vectors can be chosen in $2^p$ ways. Find $p$.
1 Answer
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· 4d ago
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Answer: $p=5$.
$\binom83=56$ triples; the coplanar (linearly dependent) ones — those containing an antipodal pair — number $4\cdot6=24$. Non-coplanar $=32=2^5$, so $p=5$.
JEE Advanced 2013 · Permutations and Combinations — verified solution by the Vidaara Team.
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