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Mathematics Question on Vectors

Let the vectors a⃗=(1+t)i^+(1−t)j^+k^,\vec{a}=(1+t) \hat{i}+(1-t) \hat{j}+\hat{k},

b→=(1−t)i^+(1+t)j^+2k^\overrightarrow{ b }=(1-t) \hat{i}+(1+t) \hat{j}+2 \hat{k} and

\vec{c}=t \hat{i}-t \hat{j}+\hat{k},$$t \in R be such that for

α,β,γ∈R,αa⃗+βb⃗+γc⃗=0→⇒α=β=γ=0\alpha, \beta, \gamma \in R, \alpha \vec{a}+\beta \vec{b}+\gamma \vec{c}=\overrightarrow{0} \Rightarrow \alpha=\beta=\gamma=0

Then, the set of all values of t is :

A

a non-empty finite set

B

equal to NN

C

equal to R−0R -\\{0\\}

D

equal to RR

Answer

equal to R−0R -\\{0\\}

Explanation

Solution

The correct option is (C): equal to R−0R -\\{0\\}