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Line (x-4)/1 = (y-2)/1 = (z-m)/2 lies in the plane 2x - 4y + z = 7: find m

The same question, asked 3 times: 3 May 2023 S1*, 9 May 2023 S1*, 9 May 2023 S2. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S1

    137
    The value of m, such that x−41=y−21=2z−m3\frac{x-4}{1}=\frac{y-2}{1}=\frac{2z-m}{3} lies in the plane 2x−5y+2z=72x-5y+2z=7, is

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  2. Question 2

    9 May 2023 S1

    129
    The value of m, such that x−41=y−21=z−m2\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2} lies in the plane 2x−4y+z=72x-4y+z=7, is

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  3. Question 3

    9 May 2023 S2

    121
    The value of m such that x−41=y−21=z+m2\frac{x-4}{1} = \frac{y-2}{1} = \frac{z+m}{2} lies in the plane 2x−4y+z=72x-4y+z=7 is

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