Let the position vectors of the vertices $A , B$ and $C$ of a triangle be $2 \hat { i } + 2 \hat { j } + \hat { k } , \hat { i } + 2 \hat { j } + 2 \hat { k }$ and $2 \hat { i } + \hat { j } + 2 \hat { k }$ respectively. Let $l _ { 1 } , l _ { 2 }$ and $l _ { 3 }$ be the lengths of perpendiculars drawn from the ortho centre of the triangle on the sides $A B , B C$ and $C A$ respectively, then $l _ { 1 } ^ { 2 } + l _ { 2 } ^ { 2 } + l _ { 3 } ^ { 2 }$ equals : (1) $\frac { 1 } { 5 }$ (2) $\frac { 1 } { 2 }$ (3) $\frac { 1 } { 4 }$ (4) $\frac { 1 } { 3 }$
Let the position vectors of the vertices $A , B$ and $C$ of a triangle be $2 \hat { i } + 2 \hat { j } + \hat { k } , \hat { i } + 2 \hat { j } + 2 \hat { k }$ and $2 \hat { i } + \hat { j } + 2 \hat { k }$ respectively. Let $l _ { 1 } , l _ { 2 }$ and $l _ { 3 }$ be the lengths of perpendiculars drawn from the ortho centre of the triangle on the sides $A B , B C$ and $C A$ respectively, then $l _ { 1 } ^ { 2 } + l _ { 2 } ^ { 2 } + l _ { 3 } ^ { 2 }$ equals :\\
(1) $\frac { 1 } { 5 }$\\
(2) $\frac { 1 } { 2 }$\\
(3) $\frac { 1 } { 4 }$\\
(4) $\frac { 1 } { 3 }$