determinar equação da reta

\(\[\begin{align} & s:\text{ }X\text{ }=\text{ }\left( 1,0,1 \right)\text{ }+\text{ }h\left( \surd 2,3+\surd 2,-3+\surd 2 \right) \\ & s\acute{\ }:\text{ }X\text{ }=\text{ }\left( 1,0,1 \right)+\text{ }h\left( -\surd 2,3-\surd 2,-3-\surd 2 \right) \\ & r:\text{ }\left( 1,1,0 \right)\text{ }+\text{ }t*\left[ \text{ }\left( 1,1,0 \right)\text{ }-\text{ }\left( 0,0,-1 \right)\text{ } \right] \\ & r:\text{ }\left( 1,1,0 \right)\text{ }+\text{ }t*\left( 1,1,1 \right) \\ & \left( 1,1,1 \right)*\left( w,v,z \right)\text{ }=\text{ }\surd 3*\surd \left( w{}^\text{2}+v{}^\text{2}+z{}^\text{2} \right)*\left( 1/2 \right) \\ & \left( w+v+z \right)/\surd \left( w{}^\text{2}+v{}^\text{2}+z{}^\text{2} \right)\text{ }=\text{ }\surd 3/2\text{ }\left( I \right) \\ & vetor\text{ }s\text{ }=\text{ }\left( w,v,z \right)\text{ }=\text{ }\left( t,1+t,-1+t \right)\text{ }=\text{ }\left( \surd 2/3,\text{ }1+\surd 2/3,\text{ }-1+\surd 2/3 \right) \\ & vetor\text{ }s\text{ }=\text{ }\left( w,v,z \right)\text{ }=\text{ }\left( t,1+t,-1+t \right)\text{ }=\text{ }\left( -\surd 2/3,\text{ }1-\surd 2/3,\text{ }-1-\surd 2/3 \right) \\ & s:\text{ }\left( 1,0,1 \right)\text{ }+\text{ }h'\left( \surd 2/3,\text{ }1+\surd 2/3,\text{ }-1+\surd 2/3 \right) \\ & s\acute{\ }:\text{ }\left( 1,0,1 \right)+\text{ }h'\left( -\surd 2/3,\text{ }1-\surd 2/3,\text{ }-1-\surd 2/3 \right) \\ \end{align}\] \)

https://www.google.com/search?q=equacao+da+reta&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjVvfvMuNnaAhUFfpAKHXDQBDUQ_AUICygC&biw=1264&bih=684#imgrc=DqS_W52tLIYB1M: