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Plane containing a given line and a given point

This type of question, asked 5 times: 21 Apr 2025 S1, 23 Apr 2025 S1, 13 Apr 2026 S1, 20 Apr 2026 S2, 13 May 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    21 Apr 2025 S1

    141
    The equation of the plane containing the line x−23=y+12=z−4−2\frac{x- 2}{3}=\frac{y+ 1}{2}=\frac{z- 4}{- 2} and the point (0,5,0)(0,5,0) is

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  2. Question 2

    23 Apr 2025 S1

    150
    The equation of the plane containing the line x+12=y+21=z−23\frac{x+ 1}{2}=\frac{y+ 2}{1}=\frac{z- 2}{3} and the point (1,−1,3)(1, - 1,3) is

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  3. Question 3

    13 Apr 2026 S1

    94
    Let a plane P pass through the point (3,7,−7)(3, 7, -7) and contain the line x−2−3=y−32=z+21\dfrac{x - 2}{-3} = \dfrac{y - 3}{2} = \dfrac{z + 2}{1}. If the distance of the plane P from the origin is d, then d2d^2 is

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  4. Question 4

    20 Apr 2026 S2

    93
    If the perpendicular distance of the plane passing through the point Q(1,0,−1)Q(1, 0, -1) and containing the line r⃗=(i^−3j^+k^)+λ(2i^−2j^+k^)\vec{r} = (\hat{i} - 3\hat{j} + \hat{k}) + \lambda(2\hat{i} - 2\hat{j} + \hat{k}) from origin is p53\dfrac{p}{\sqrt{53}} then p=p = ...

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  5. Question 5

    13 May 2026 S1

    91
    The equation of the plane passing through the point (0,4,3)(0, 4, 3) and containing the line x−11=y−33=z−22\dfrac{x - 1}{1} = \dfrac{y - 3}{3} = \dfrac{z - 2}{2} is ax+by+cz+d=0ax + by + cz + d = 0, (a≥0)(a \ge 0). The value of (a+b+c+d)(a + b + c + d) is

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