A pyramid with vertex at the point

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

P

, whose position vector is

4\hat{i} + 2\hat{j} + 2\sqrt{3}\hat{k}

has a regular hexagonal base

ABCDEF

. Position vectors of points

A

and

B

are

\hat{i}

and

\hat{i} + 2\hat{j}

, respectively. Centre of the base has the position vector

\hat{i} + \hat{j} + \sqrt{3}\hat{k}

. Altitude drawn from

P

on the base meets the diagonal

AD

at point

G

. Find all possible position vectors of

G

. It is given that volume of the pyramid is

6\sqrt{3}

cu units.