The position vectors of points $AandB$ w.r.t. the origin are $\vec{a}=\hat{i}+3\hat{j}-2\hat{k}$, $\vec{b}=3\hat{i}+\hat{j}-2\hat{k}$ respectively. Determine vector $\vec{O}P$ which bisects angle $AOB,$ where $P$ is a point on $AB\dot{}$

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