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Question

If the lines x12=y+13=z14 and x31=yk2=z1 intersect, then the value of k is -


A

32

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B

92

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C

29

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D

32

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Solution

The correct option is B

92


Since the lines intersect, therefore they must have a point in common, i.e.
x12=y+13=z14=λandx31=yk2=z1=μx=2λ+1,y=3λ1z=4λ+1
and x=μ+3,y=2μ+k,z=μ are same.
2λ+1=μ+33λ1=2μ+k4λ+1=μ
On solving these equations, we get,
λ=32 and μ=5k=3λ2μ1k=3(32)2(5)1=92k=92


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