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Lines (x-1)/2 = (y+1)/3 = (z-1)/4 and (x-3)/1 = (y-k)/2 = z/1 intersect: find k

The same question, asked 7 times: 10 May 2023 S1*, 10 May 2023 S2*, 15 May 2023 S2*, 11 May 2024 S2*, 14 May 2024 S2*, 23 Apr 2025 S1*, 11 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2023 S1

    122
    If the lines x−12=y−23=z−14\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-1}{4} and x−3−1=y−k2=z1\frac{x-3}{-1}=\frac{y-k}{2}=\frac{z}{1} intersect, then k is equal to

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  2. Question 2

    10 May 2023 S2

    126
    If the line x−12=y+13=z−14\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} and x−31=y−k2=z1\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1} intersect, then the value of k is

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  3. Question 3

    15 May 2023 S2

    127
    If the lines x−12=y+23=z−14\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-1}{4} and x−31=y−k2=z1\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1} intersect, then kk has the value

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  4. Question 4

    11 May 2024 S2

    104
    If the lines x−12=y+13=z−14\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} and x−31=y−k2=z1\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1} intersect, then the value of k is:

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  5. Question 5

    14 May 2024 S2

    137
    If the lines x−k2=y+13=z−14\frac{x-k}{2}=\frac{y+1}{3}=\frac{z-1}{4} and x−31=y−9/22=z1\frac{x-3}{1}=\frac{y-9/2}{2}=\frac{z}{1} intersect, then the value of kk is

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  6. Question 6

    23 Apr 2025 S1

    138
    If the lines x−12=y+13=z−14\frac{x- 1}{2}=\frac{y+ 1}{3}=\frac{z- 1}{4} and x−31=y−k2=z1\frac{x- 3}{1}=\frac{y- k}{2}=\frac{z}{1}. intersect, then the value of k is

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  7. Question 7

    11 Apr 2026 S1

    94
    If the lines x−12=y+13=z−14\dfrac{x - 1}{2} = \dfrac{y + 1}{3} = \dfrac{z - 1}{4} and x−21=y+m2=z−21\dfrac{x - 2}{1} = \dfrac{y + m}{2} = \dfrac{z - 2}{1} intersect each other, then the value of mm is....

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