MathematicsMedium202×since 2002Q5696Let the vectors a⃗=(1+t)i^+(1−t)j^+k^,b⃗=(1−t)i^+(1+t)j^+2k^\vec{a}=(1+t) \hat{i}+(1-t) \hat{j}+\hat{k}, \vec{b}=(1-t) \hat{i}+(1+t) \hat{j}+2 \hat{k}a=(1+t)i^+(1−t)j^+k^,b=(1−t)i^+(1+t)j^+2k^ and c⃗=ti^−tj^+k^,t∈R\vec{c}=t \hat{i}-t \hat{j}+\hat{k}, t \in \mathbf{R}c=ti^−tj^+k^,t∈R be such that for α,β,γ∈R,αa⃗+βb⃗+γc⃗=0→⇒α=β=γ=0\alpha, \beta, \gamma \in \mathbf{R}, \alpha \vec{a}+\beta \vec{b}+\gamma \vec{c}=\overrightarrow{0} \Rightarrow \alpha=\beta=\gamma=0α,β,γ∈R,αa+βb+γc=0⇒α=β=γ=0. Then, the set of all values of ttt is :Aa non-empty finite setBequal to N\mathbf{N}NCequal to R−{0}\mathbf{R}-\{0\}R−{0}Dequal to R\mathbf{R}RCheck answerSkip