Given the lines $r _ { 1 } \equiv \left\{ \begin{array} { l } 6 x - y - z = 1 , \\ 2 x - y + z = 1 \end{array} \quad \right.$ and $r _ { 2 } \equiv \left\{ \begin{array} { l } 3 x - 5 y - 2 z = 3 , \\ 3 x + y + 4 z = 3 \end{array} \right.$ it is requested:\ a) (1 point) Study the relative position of $r _ { 1 }$ and $r _ { 2 }$.\ b) (1 point) Calculate the distance between the two lines.\ c) (1 point) Find the equation of the plane that contains $r _ { 1 }$ and the point $\mathrm { P } ( 1,2,3 )$.
Given the lines $r _ { 1 } \equiv \left\{ \begin{array} { l } 6 x - y - z = 1 , \\ 2 x - y + z = 1 \end{array} \quad \right.$ and $r _ { 2 } \equiv \left\{ \begin{array} { l } 3 x - 5 y - 2 z = 3 , \\ 3 x + y + 4 z = 3 \end{array} \right.$ it is requested:\
a) (1 point) Study the relative position of $r _ { 1 }$ and $r _ { 2 }$.\
b) (1 point) Calculate the distance between the two lines.\
c) (1 point) Find the equation of the plane that contains $r _ { 1 }$ and the point $\mathrm { P } ( 1,2,3 )$.