If \( \vec{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \ha...

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If \( \vec{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+\hat{k} \) and \( \vec{c}=3 \hat{i}+\hat{j} \) are such that \( \vec{a}+\lambda \vec{b} \) is perpendicular to \( \vec{c} \), then find the value of \( \lambda \).
\( \mathrm{P} \)
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