The direction cosines of the line of intersection of two planes x−y+z−5=0,x−3y−6=0 are

The direction ratios of line of intersection of two planes are proportional to the vector which is perpendicular to both normal vectors of the planesThe given planes are x−y+z−5=0,x−3y−6=0Its normal vectors are i−j+k,i−3jvector perpendicular to both the vectors is ijk1−111−30=i(3)−j(−1)+k(−2)=3i−j−2kThe line of intersection of two planes having direction ratios ⟨3,−1,−2⟩ and its direction cosines are ⟨314,−114,−214⟩