A pyramid with vertex at point `P` has a regular hexagonal base `A B C D E F` , Position vector of points A and B are `hat i and hat i + 2 hat j` The centre of base has the position vector ` hat i+ hat j+sqrt(3) hat kdot` Altitude drawn from `P` on the base meets the diagonal `A D` at point `Gdot` find the all possible position vectors of `Gdot` It is given that the volume of the pyramid is `6sqrt(3)` cubic units and `A P` is 5 units.