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Plane containing a given line and perpendicular to a given plane

This type of question, asked 5 times: 3 May 2023 S1, 3 May 2023 S2, 12 May 2024 S2, 23 Apr 2025 S1, 15 May 2026 S2. All 5 questions 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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  5. Question 5

    15 May 2026 S2

    93
    The equation of the plane containing the line rˉ=(2i^−k^)+λ(i^+j^+2k^)\bar{r} = (2\hat{i} - \hat{k}) + \lambda(\hat{i} + \hat{j} + 2\hat{k}) and perpendicular to the plane rˉ⋅(3i^−j^+k^)=20\bar{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 20 is…\ldots

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