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Let the position vectors of points ‘A’ and ‘B’ be $\hat{i} + \hat{j} + \hat{k}$ and $2\hat{i} + \hat{j} + 3\hat{k}$, respectively. A point ‘P’ divides the line segment AB internally in the ratio $\lambda : 1$ $(\lambda > 0)$. If O is the region and $\overrightarrow{OB} \cdot \overrightarrow{OP} - 3|\overrightarrow{OA} \times \overrightarrow{OP}|^2 = 6$, then $\lambda$ is equal to _____.
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