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Vector Algebra question

2022 · 28 Jul · Shift 1 · Q25

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JEE Main
Mathematics
Vector Algebra
2022 · 28 Jul · Shift 1 · Q25

Vector Algebra question

2022 · 28 Jul · Shift 1 · Q25

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let the vectors

\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}

and

\vec{c}=t \hat{i}-t \hat{j}+\hat{k}, t \in \mathbf{R}

be such that for

\alpha, \beta, \gamma \in \mathbf{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 $\mathbf{N}$
C
equal to $\mathbf{R}-\{0\}$
D
equal to $\mathbf{R}$

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