Plane through a point perpendicular to two given planes
This type of question, asked 7 times: 3 May 2023 S2, 4 May 2023 S1, 9 May 2023 S1, 9 May 2023 S2, 14 May 2024 S1, 19 Apr 2025 S1, 15 Apr 2026 S2. All 7 questions below, oldest first.
Try each one first, then open its answer.
Question 1
3 May 2023 S2
126
The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x−y−2z=5 and 3x−6y+2z=7 is
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Question 2
4 May 2023 S1
137
A plane which is perpendicular to two planes 2x−2y+z=0 and x−y+2z=4, passes through (1,−2,1). The distance of the plane from the point (1,2,2) is
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Question 3
9 May 2023 S1
111
The equation of the plane, passing through the point (1,1,1) and perpendicular to the planes 2x+y−2z=5 and 3x−6y−2z=7, is
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Question 4
9 May 2023 S2
117
A plane which is perpendicular to two planes 2x−2y+z=0 and x−y+2z=4, passes through (1,−2,1). The distance of the plane from the point (1,2,2) is
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Question 5
14 May 2024 S1
121
Equation of the plane passing through (1,−1,2) and perpendicular to the planes x+2y−2z=4 and 3x+2y+z=6 is:
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Question 6
19 Apr 2025 S1
105
A plane passes through (1,−2,1) and is perpendicular to the planes 2x−2y+z=0 and x−y+2z=4. The distance of the point (1,2,2) from this plane is ____ units.
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Question 7
15 Apr 2026 S2
95
The equation of the plane passing through the point (1,2,1) and perpendicular to the planes x+2y+2z−7=0 and 3x+3y+2z−5=0 is
