A pyramid with vertex at point $P$ has a regular hexagonal base $ABCDEF$ , Positive vector of points A and B are $\hat{i}\text{and}\hat{i}+2\hat{j}$ The centre of base has the position vector $\hat{i}+\hat{j}+\sqrt{3}\hat{k}\dot{}$ Altitude drawn from $P$ on the base meets the diagonal $AD$ at point $G\dot{}$ find the all possible position vectors of $G\dot{}$ It is given that the volume of the pyramid is $6\sqrt{3}$ cubic units and $AP$ is 5 units.

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