Q. 23

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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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