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Plane through three given points

This type of question, asked 3 times: 2 May 2023 S1, 26 Apr 2025 S2, 19 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    2 May 2023 S1

    135
    The Cartesian equation of the plane, passing through the points (3,1,1)(3,1,1), (1,2,3)(1,2,3) and (−1,4,2)(-1,4,2), is

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  2. Question 2

    26 Apr 2025 S2

    143
    The direction cosines of a normal to the plane passing through (4,2,3),(−1,4,2)(4,2,3),( - 1,4,2) and (3,2,1)(3,2,1) are... .

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  3. Question 3

    19 Apr 2026 S2

    91
    The perpendicular distance from the origin to the plane containing the points (1,−2,1),(2,−1,−3)(1, -2, 1), (2, -1, -3) and (0,1,5)(0, 1, 5) is...(in units)

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