Answer :

The direction ratios of a line, if the cartesian equation of the line is given , is a,b,c.


Hence, the direction ratios of line L:



and the direction ratios of line M:



two lines with direction ratios, a1, a2, a3 and b1, b2, b3, are perpendicular if and only if a1b1+a2b2+a3b3=0


Hence,


Solving this equation, we get


Hence, the equation of lines are:




Any general point on line will be


and on the line will be .


For the lines to intersect, . Solving the equations for x and y-coordinates,



we get and m=1.


Equating equations for z-coordinates, we get


3k+3 = 5m+6


Substituting and m=1, we get


or 15=22 which is not true.


Hence, the lines do not intersect in real space.


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