The given line has direction vector v=(2,3,−2) We seek a direction d=(d1,d2,d3) with v⋅d=2d1+3d2−2d3=0 One convenient choice is d1=−3,‌‌d2=4,‌‌d3=3 since 2(−3)+3(4)−2(3)=−6+12−6=0. Hence the required line through (0,1,2) is ‌