In a four-dimensional space where unit vectors along the axes are \...

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In a four-dimensional space where unit vectors along the axes are \( \hat{i}, \hat{j}, \hat{k} \) and \( \hat{l} \), and \( \overrightarrow{a_{1}}, \overrightarrow{a_{2}}, \overrightarrow{a_{3}}, \overrightarrow{a_{4}} \)
\( \mathrm{P} \) are four non-zero vectors such that no vector can be expressed as a linear combination of others and \( (\lambda-1)\left(\vec{a}_{1}-\vec{a}_{2}\right)+\mu\left(\overrightarrow{a_{2}}+\overrightarrow{a_{3}}\right)+\gamma\left(\overrightarrow{a_{3}}+\overrightarrow{a_{4}}-2 \overrightarrow{a_{2}}\right)+\overrightarrow{a_{3}}+\delta \overrightarrow{a_{4}}=\overrightarrow{0} \), then
W
(1) \( \lambda=1 \)
(2) \( \mu=-2 / 3 \)
(3) \( \gamma=2 / 3 \)
(4) \( \delta=1 / 3 \)
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