JEE Advanced 2025 | PAPER 1 - QUESTION NUMBER 16 | Vectors | Xylem JEEnius

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Let \(\mathbf w=\hat i+\hat j-2\hat k\), and \(\mathbf u,\mathbf v\in\mathbb R^3\) satisfy
\(\mathbf u\times\mathbf v=\mathbf w\), \(\mathbf v\times\mathbf w=\mathbf u\).
Write \(\mathbf u=(\alpha,\beta,\gamma)\) and let \(t\in\mathbb R\) satisfy
\[
- t\alpha+\beta+\gamma=0,\quad\alpha-t\beta+\gamma=0,\quad\alpha+\beta-t\gamma=0.
\]
Match the provided expressions to numeric options.

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