Hello,
I don't know if you know scalar product, vectors.
(a,b,c)*(3,7,1)=0==>3a+7b+c=0 (1)
(a,b,c)*(-1,1,0)=0==>-a+b=0 (2)
Let's r a real number:
a=r
from (2) : b=a=r
from (3) : 3r+7r+c=0==>c=-10r
a vector X is (a,b,c)= (r,r,-10r) = r(1,1,-10)
But ||X||²=r²*(1²+1²+(-10)²)=r²*102
(X=+1/√102 * (1,1,-10) ) or ( X=-1/√102 *(1,1,-10) )
