In a four - dimensional space where unit vectors \( \mathrm{P} \) a...

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