Let $O$ be the origin. Let $\overrightarrow { O P } = x \hat { i } + y \hat { j } - \widehat { k }$ and $\overrightarrow { O Q } = - \hat { i } + 2 \hat { j } + 3 x \hat { k } , x , y \in R , x > 0$, be such that $| \overrightarrow { P Q } | = \sqrt { 20 }$ and the vector $\overrightarrow { O P }$ is perpendicular to $\overrightarrow { O Q }$. If $\overrightarrow { O R } = 3 \hat { i } + \mathrm { z } \hat { j } - 7 \hat { k } , z \in R$, is coplanar with $\overrightarrow { O P }$ and $\overrightarrow { O Q }$, then the value of $x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ is equal to (1) 7 (2) 9 (3) 2 (4) 1
Let $O$ be the origin. Let $\overrightarrow { O P } = x \hat { i } + y \hat { j } - \widehat { k }$ and $\overrightarrow { O Q } = - \hat { i } + 2 \hat { j } + 3 x \hat { k } , x , y \in R , x > 0$, be such that $| \overrightarrow { P Q } | = \sqrt { 20 }$ and the vector $\overrightarrow { O P }$ is perpendicular to $\overrightarrow { O Q }$. If $\overrightarrow { O R } = 3 \hat { i } + \mathrm { z } \hat { j } - 7 \hat { k } , z \in R$, is coplanar with $\overrightarrow { O P }$ and $\overrightarrow { O Q }$, then the value of $x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ is equal to\\
(1) 7\\
(2) 9\\
(3) 2\\
(4) 1