Question
If the lines x−12=y+13=z−14 and x−31=y−k1=z1 intersect, then k =
Answer: Option B
:
B
Any point onx−12=y+13=z−14=λ is,
(2λ+1,3λ−1,4λ+1);λ∈R
Any point on x−31=y−k2=z1=μ is,
(μ+3,2μ+k,μ);μ∈R
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 −92−1=−10+k⇒k=92.
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:
B
Any point onx−12=y+13=z−14=λ is,
(2λ+1,3λ−1,4λ+1);λ∈R
Any point on x−31=y−k2=z1=μ is,
(μ+3,2μ+k,μ);μ∈R
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 −92−1=−10+k⇒k=92.
Was this answer helpful ?
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