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Plane containing a line through the origin and perpendicular to the plane containing two other lines through the origin

The same question, asked 4 times: 3 May 2023 S1*, 3 May 2023 S2*, 12 May 2024 S2*, 23 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S1

    121
    Equation of the plane containing the straight line x3=y2=z4\frac{x}{3}=\frac{y}{2}=\frac{z}{4} and perpendicular to the plane containing the straight lines x4=y3=z2\frac{x}{4}=\frac{y}{3}=\frac{z}{2} and x2=y−4=z3\frac{x}{2}=\frac{y}{-4}=\frac{z}{3} is

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  2. Question 2

    3 May 2023 S2

    135
    Equation of the plane containing the straight line x2=y3=z4\frac{x}{2}=\frac{y}{3}=\frac{z}{4} and perpendicular to the plane containing the straight lines x3=y4=z2\frac{x}{3}=\frac{y}{4}=\frac{z}{2} and x4=y2=z3\frac{x}{4}=\frac{y}{2}=\frac{z}{3} is

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  3. Question 3

    12 May 2024 S2

    123
    Equation of plane containing the line x2=y3=z4\frac{x}{2}=\frac{y}{3}=\frac{z}{4} and perpendicular to the plane containing the lines x3=y4=z2\frac{x}{3}=\frac{y}{4}=\frac{z}{2} and x4=y2=z3\frac{x}{4}=\frac{y}{2}=\frac{z}{3} is

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  4. Question 4

    23 Apr 2025 S1

    149
    The equation of the plane containing the line x1=y2=z3\frac{x}{1}=\frac{y}{2}=\frac{z}{3} and perpendicular to the plane containing the lines x2=y3=z1\frac{x}{2}=\frac{y}{3}=\frac{z}{1} and x3=y2=z1\frac{x}{3}=\frac{y}{2}=\frac{z}{1} is

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