If a line passing through (2, 1, 4) cuts off an intercept of minimum length between two non coplanar lines x−6=yα=−z  and x=y0=z   then α  is

Line passes through P2,1,4  lie along shortest distance between two non – coplanar lines L1=x−61=yα=z−1=k1⇒A6+k1,αk1,−k1L2=x1=y0=z1=k2⇒Bk2,0,k2  PA perpendicular to L1⇒6+k1−21+αk1−1α+−k1−4−1=0 α2k1−α+2k1+8=0PB is perpendicular to L2⇒k2=3AB perpendicualr to L16+k1−3+ααk1+−1−k1−3=0α2k1+2k1+6=0Hence, α=2