Find two unit vectors orthogonal to both 3, 7, 1 and −1, 1, 0. find :
(smaller i-value)
(larger i-value)

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) )