The given line has direction vectorv=(2,3,−2)We seek a direction d=(d1,d2,d3) withv⋅d=2d1+3d2−2d3=0 One convenient choice isd1=−3,d2=4,d3=3 since2(−3)+3(4)−2(3)=−6+12−6=0.Hence the required line through (0,1,2) is−3x−0=4y−1=3z−2which is Option B.