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, a_{1}, a_{2}, a_{3} and b_{1}, b_{2}, b_{3}, are perpendicular if and only if a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}=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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