Question

Let α ∈ R and the three vectors ⃗a = αî + j^ + 3k^, ⃗b = 2î + j^ - αk^ and ⃗c = αî - 2j^ + 3k^. Then the set S = (α : ⃗a, ⃗b and ⃗c are coplanar)
(A) Contains exactly two numbers only one of which is positive
(B) is empty
(C) Contains exactly two positive numbers
(D) is singleton

Answer 1

Let α ∈ R and the three vectors ⃗a = αî + j^ + 3k^, ⃗b = 2î + j^ - αk^ and ⃗c = αî - 2j^ + 3k^. Then the set S = (α : ⃗a, ⃗b and ⃗c are coplanar)

(A) Contains exactly two numbers only one of which is positive

(B) is empty❤✅

(C) Contains exactly two positive numbers

(D) is singleton

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