Let the vectors a → = 1 + t i ^ + 1 - t j ^ + k ^ , b → = 1 - t i ^ + 1 + t j ^ + 2 k ^ and c → = t i ^ - t j ^ + k ^ , t ∈ R be such that for α , β , γ ∈ R , α a → + β b → + γ c → = 0 → ⇒ α = β = γ = 0 . Then, the set of all values of t is

Step-by-step solution

Given the vectors a → = 1 + t i ^ + 1 - t j ^ + k ^ , b → = 1 - t i ^ + 1 + t j ^ + 2 k ^ and c → = t i ^ - t j ^ + k ^ ,   t ∈ R be such that for α , β , γ ∈ R ,   α a → + β b → + γ c → = 0 → ⇒ α = β = γ = 0 . Then, the set of all values of t is By its given condition : a → , b → , c → are linearly independent vectors or they are non-coplanar We know that when vectors are non-coplana