The vector equation of the line passing through (1,2,3) and parallel to the planes r¯.(i¯−j¯+2k¯)=5 and r¯.(3i¯+j¯+k¯)=6 is

a¯=i¯−j¯+2k¯;b¯=3i¯+j¯+k¯a¯×b¯=−3i¯+5j¯+4k¯line parallel to a¯×b¯ and passing through (1,2,3)r¯=(i¯+2j¯+3k¯)+λ(−3i¯+5j¯+4k¯)x=y=z...........(1)x=y2=z3...........(2)