Let α ∈ R and the three vectors a → = α i ^ + j ^ + 3 k ^ , b → = 2 i ^ + j ^ - α k ^ and c → = α i ^ - 2 j ^ + 3 k ^ . Then the set S = { α : a → , b → and c → are coplanar}

Question

Let α ∈ R and the three vectors a → = α i ^ + j ^ + 3 k ^ , b → = 2 i ^ + j ^ - α k ^ and c → = α i ^ - 2 j ^ + 3 k ^ . Then the set S = { α : a → , b → and c → are coplanar}, is singleton, contains exactly two positive numbers, is empty, contains exactly two numbers only one of which is positive

MARKS App · Accepted Answer

If a → , b → and c → are coplanar then, α 1 3 2 1 - α α - 2 3 = 0 ⇒ 3 α 2 + 18 = 0 ⇒ α ∈ ϕ

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