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Plane through (1,-2,1) perpendicular to 2x - 2y + z = 0 and x - y + 2z = 4: its distance from (1,2,2)

The same question, asked 3 times: 4 May 2023 S1, 9 May 2023 S2, 19 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S1

    137
    A plane which is perpendicular to two planes 2x−2y+z=02x-2y+z=0 and x−y+2z=4x-y+2z=4, passes through (1,−2,1)(1,-2,1). The distance of the plane from the point (1,2,2)(1,2,2) is

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  2. Question 2

    9 May 2023 S2

    117
    A plane which is perpendicular to two planes 2x−2y+z=02x-2y+z=0 and x−y+2z=4x-y+2z=4, passes through (1,−2,1)(1,-2,1). The distance of the plane from the point (1,2,2)(1,2,2) is

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  3. Question 3

    19 Apr 2025 S1

    105
    A plane passes through (1,−2,1)(1, - 2,1) and is perpendicular to the planes 2x−2y+z=02x- 2y+z= 0 and x−y+2z=4x-y+ 2z = 4. The distance of the point (1,2,2)(1,2,2) from this plane is ____\_\_\_\_ units.

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