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JEE Advanced2013MathematicsVector AlgebraActual

Consider the set of eight vectors V = a i ^ + b j ^ + c k ^ : a, b, c ∈ - 1 , 1 . Three non-coplanar vectors can be chosen from V in 2 p ways. Then p is

Correct answer

5

Step-by-step solution

x → ≡ i ^ + j ^ + k ^ y → ≡ i ^ + j ^ - k ^ z → ≡ i ^ + j ^ + k ^ ω → = i ^ - j ^ - k ^ x ¯ ′ = - i ^ - j ^ - k ^ y → ′ = - i ^ - j ^ + k ^ z → ′ = - i ^ + j ^ - k ^ ω → ′ = - i ^ + j ^ + k ^ If we take x → , x → ′ and any one of remaining six, vectors will always be coplanar ∴ No. of coplanar vectors = 6 Similarly on taking y → , y → ′ = 6 z , z → ′ = 6 ω , ω &

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