Question:
If a plane passing through the point \( (2, 2, 1) \) and is perpendicular to the planes \( 3x + 2y + 4z = 10 \) and \( 2x + y + 3z = 2 \), then the equation of the plane is
If a plane passing through the point \( (2, 2, 1) \) and is perpendicular to the planes \( 3x + 2y + 4z = 10 \) and \( 2x + y + 3z = 2 \), then the equation of the plane is
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The equation of a plane passing through a point can be written as \( (x - x_0)(a) + (y - y_0)(b) + (z - z_0)(c) = 0 \), where \( a, b, c \) are the normal vector components.
Updated On: Jan 12, 2026
- \( 2x - y - z = 0 \)
- \( 3x + 2y + z = 0 \)
- \( x + y + z = 1 \)
- \( x + y + 2z = 1 \)
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The Correct Option is A
Solution and Explanation
The equation of the plane is derived by using the perpendicular condition with respect to the two given planes, and using the point \( (2, 2, 1) \).
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