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Lines (x-2)/1 = (y-3)/1 = (z-4)/-k and (x-1)/k = (y-4)/2 = (z-5)/1 are coplanar: find k

The same question, asked 3 times: 4 May 2023 S1, 19 Apr 2025 S2*, 16 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S1

    102
    The lines x−21=y−31=z−4−k\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k} and x−1k=y−42=z−51\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1} are coplanar if

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  2. Question 2

    19 Apr 2025 S2

    142
    The lines x−31=y−21=z−5−k\frac{x- 3}{1}=\frac{y- 2}{1}=\frac{z- 5}{-k} and x−4k=y−31=z−32\frac{x- 4}{k}=\frac{y- 3}{1}=\frac{z - 3}{2} are coplanar, hence k=k =

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  3. Question 3

    16 Apr 2026 S1

    90
    The lines x−21=y−31=z−4−k\dfrac{x - 2}{1} = \dfrac{y - 3}{1} = \dfrac{z - 4}{-k} and x−1k=y−42=z−51\dfrac{x - 1}{k} = \dfrac{y - 4}{2} = \dfrac{z - 5}{1} are coplanar if

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