Let the position vectors of two points $P$ and $Q$ be $3 \hat { \mathrm { i } } - \hat { \mathrm { j } } + 2 \widehat { \mathrm { k } }$ and $\hat { \mathrm { i } } + 2 \hat { \mathrm { j } } - 4 \widehat { \mathrm { k } }$, respectively. Let $R$ and $S$ be two points such that the direction ratios of lines $P R$ and $Q S$ are $( 4 , - 1,2 )$ and $( - 2,1 , - 2 )$, respectively. Let lines $P R$ and $Q S$ intersect at $T$. If the vector $\overrightarrow { T A }$ is perpendicular to both $\overrightarrow { P R }$ and $\overrightarrow { Q S }$ and the length of vector $\overrightarrow { T A }$ is $\sqrt { 5 }$ units, then the modulus of a position vector of $A$ is : (1) $\sqrt { 482 }$ (2) $\sqrt { 171 }$ (3) $\sqrt { 5 }$ (4) $\sqrt { 227 }$
Let the position vectors of two points $P$ and $Q$ be $3 \hat { \mathrm { i } } - \hat { \mathrm { j } } + 2 \widehat { \mathrm { k } }$ and $\hat { \mathrm { i } } + 2 \hat { \mathrm { j } } - 4 \widehat { \mathrm { k } }$, respectively. Let $R$ and $S$ be two points such that the direction ratios of lines $P R$ and $Q S$ are $( 4 , - 1,2 )$ and $( - 2,1 , - 2 )$, respectively. Let lines $P R$ and $Q S$ intersect at $T$. If the vector $\overrightarrow { T A }$ is perpendicular to both $\overrightarrow { P R }$ and $\overrightarrow { Q S }$ and the length of vector $\overrightarrow { T A }$ is $\sqrt { 5 }$ units, then the modulus of a position vector of $A$ is :\\
(1) $\sqrt { 482 }$\\
(2) $\sqrt { 171 }$\\
(3) $\sqrt { 5 }$\\
(4) $\sqrt { 227 }$