Let the position vectors of the vertices $A , B$ and $C$ of a tetrahedron $A B C D$ be $\hat { \mathbf { i } } + 2 \hat { \mathbf { j } } + \hat { \mathbf { k } } , \hat { \mathbf { i } } + 3 \hat { \mathbf { j } } - 2 \hat { k }$ and $2 \hat { i } + \hat { j } - \hat { k }$ respectively. The altitude from the vertex $D$ to the opposite face $A B C$ meets the median line segment through $A$ of the triangle $A B C$ at the point $E$. If the length of $A D$ is $\frac { \sqrt { } \overline { 110 } } { 3 }$ and the volume of the tetrahedron is $\frac { \sqrt { 805 } } { 6 \sqrt { 2 } }$, then the position vector of $E$ is (1) $\frac { 1 } { 12 } ( 7 \hat { \mathbf { i } } + 4 \hat { \mathbf { j } } + 3 \hat { k } )$ (2) $\frac { 1 } { 2 } ( \hat { i } + 4 \hat { j } + 7 \hat { k } )$ (3) $\frac { 1 } { 6 } ( 12 \hat { i } + 12 \hat { j } + \hat { k } )$ (4) $\frac { 1 } { 6 } ( 7 \hat { \mathrm { i } } + 12 \hat { \mathrm { j } } + \hat { \mathrm { k } } )$
Let the position vectors of the vertices $A , B$ and $C$ of a tetrahedron $A B C D$ be $\hat { \mathbf { i } } + 2 \hat { \mathbf { j } } + \hat { \mathbf { k } } , \hat { \mathbf { i } } + 3 \hat { \mathbf { j } } - 2 \hat { k }$ and $2 \hat { i } + \hat { j } - \hat { k }$ respectively. The altitude from the vertex $D$ to the opposite face $A B C$ meets the median line segment through $A$ of the triangle $A B C$ at the point $E$. If the length of $A D$ is $\frac { \sqrt { } \overline { 110 } } { 3 }$ and the volume of the tetrahedron is $\frac { \sqrt { 805 } } { 6 \sqrt { 2 } }$, then the position vector of $E$ is\\
(1) $\frac { 1 } { 12 } ( 7 \hat { \mathbf { i } } + 4 \hat { \mathbf { j } } + 3 \hat { k } )$\\
(2) $\frac { 1 } { 2 } ( \hat { i } + 4 \hat { j } + 7 \hat { k } )$\\
(3) $\frac { 1 } { 6 } ( 12 \hat { i } + 12 \hat { j } + \hat { k } )$\\
(4) $\frac { 1 } { 6 } ( 7 \hat { \mathrm { i } } + 12 \hat { \mathrm { j } } + \hat { \mathrm { k } } )$