Let \( \vec{x} \) be a vector in the plane containing vectors \( \v...

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Let \( \vec{x} \) be a vector in the plane containing vectors \( \vec{a}=2 \hat{i}-\hat{j}+\hat{k} \) and \( \vec{b}=\hat{i}+2 \hat{j}-\hat{k} \). If the vector \( \vec{x} \) is
P perpendicular to \( (3 \hat{i}+2 \hat{j}-\hat{k}) \) and its projection on \( \vec{a} \) is \( \frac{17 \sqrt{6}}{2} \), then the value of \( |\vec{x}|^{2} \) is equal to
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