For the lines x2=y−3=z1 and x−23=y−1−5=z+22

Dr’s of line of shortest distance are 1 3 , 1 3 , 1 3 , Line of shortest distance pass through the point 21 , − 92 3 , 32 3 , Equation of line of shortest distance is 3 ( x − 21 ) = 3 y + 92 = 3 z − 32 , Drs of line of shortest distance are ( 2 , 2 , 2 )

For the lines x2=y−3=z1 and x−23=y−1−5=z+22

Dr’s of line of shortest distance are 1 3 , 1 3 , 1 3

Line of shortest distance pass through the point 21 , − 92 3 , 32 3

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For the lines $\frac{x}{2} = \frac{y}{- 3} = \frac{z}{1}$ and $\frac{x - 2}{3} = \frac{y - 1}{- 5} = \frac{z + 2}{2}$

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Dr’s of line of shortest distance are $(\frac{1}{3}, \frac{1}{3}, \frac{1}{3})$

Line of shortest distance pass through the point $(21, \frac{- 92}{3}, \frac{32}{3})$

Equation of line of shortest distance is $3 (x - 21) = 3 y + 92 = 3 z - 32$

Drs of line of shortest distance are $(2, 2, 2)$

answer is A, B, C, D.

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Detailed Solution

Let $P (2 r_{1}, - 3 r_{1}, r_{1})$ and $Q (3 r_{2} + 2, - 5 r_{2} + 1, 2 r_{2} - 2)$ be any two points on lines, So that PQ line of shortest distance.