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Which is an implicit equation for the plane through the point (-9,2, 9) and perpendicular to the plane 3x -6y - 52 = 0

Which is an implicit equation for the plane through the point (-9,2, 9) and perpendicular to the plane 3x -6y - 52 = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
**Determining the Implicit Equation of a Plane** We are tasked with finding the implicit equation of a plane. The plane must pass through the point \((-9, 2, 9)\) and be perpendicular to the given plane described by the equation \(3x - 6y - 5z = 0\). **Key Concepts:** - **Implicit Equation of a Plane:** This is generally expressed in the form \(Ax + By + Cz = D\), where \((A, B, C)\) provides the normal vector to the plane. - **Normal Vector:** The direction perpendicular to the plane. In this scenario, the normal vector of the desired plane will be parallel to the vector \((3, -6, -5)\) from the given plane's equation. **Steps to Find the Equation:** 1. Use the normal vector \((3, -6, -5)\) for the plane since it must be perpendicular to the given plane. 2. Apply point \((-9, 2, 9)\) to satisfy the plane equation. This structured approach will allow for determining the implicit equation efficiently.
Transcribed Image Text:**Determining the Implicit Equation of a Plane** We are tasked with finding the implicit equation of a plane. The plane must pass through the point \((-9, 2, 9)\) and be perpendicular to the given plane described by the equation \(3x - 6y - 5z = 0\). **Key Concepts:** - **Implicit Equation of a Plane:** This is generally expressed in the form \(Ax + By + Cz = D\), where \((A, B, C)\) provides the normal vector to the plane. - **Normal Vector:** The direction perpendicular to the plane. In this scenario, the normal vector of the desired plane will be parallel to the vector \((3, -6, -5)\) from the given plane's equation. **Steps to Find the Equation:** 1. Use the normal vector \((3, -6, -5)\) for the plane since it must be perpendicular to the given plane. 2. Apply point \((-9, 2, 9)\) to satisfy the plane equation. This structured approach will allow for determining the implicit equation efficiently.
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