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Question

If the lines x12=y+13=z14 and x31=yk1=z1 and intersect, then k =
[IIT Screening 2004]


A

29

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B

29

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C

0

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D

None of these

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Solution

The correct option is B

29


Any point on x12=y+13=z14=μ is, μ+3,2μ+k,μ);μϵR
The given lines intersect if and only if the system of equations (in λ and μ)
2λ+1=μ+3 ....(i)
3λ-1=2μ+k ....(ii)
4λ+1=μ .....(iii)
has a unique solution.
Solving (i) and (iii), we get λ=32,μ=5
From (ii), we get 921=10+kk=92


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