How To Find The Equation of a Plane Given a Point and Perpendicular Normal Vector | Summary and Q&A

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December 5, 2019
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The Organic Chemistry Tutor
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How To Find The Equation of a Plane Given a Point and Perpendicular Normal Vector

TL;DR

Learn how to find the equation of a plane using a given point and a vector that is perpendicular to the plane.

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Questions & Answers

Q: What are the two things needed to define a plane?

A point on the plane and a vector that is perpendicular to it.

Q: How can you determine if two vectors are orthogonal or perpendicular?

If the dot product of the two vectors equals zero, they are orthogonal or perpendicular to each other.

Q: How do you find the equation of a plane using a point and normal vector?

Using the formula A(X - X0) + B(Y - Y0) + C(Z - Z0) = 0, where A, B, and C are the components of the normal vector, and X0, Y0, and Z0 are the coordinates of the point.

Q: Can you provide an example of finding the equation of a plane?

Let's say A is 3, B is 6, C is 5, X0 is 2, Y0 is -5, and Z0 is 3. Plugging these values into the formula, we get 3x + 6y + 5z = -9 as the equation of the plane.

Summary & Key Takeaways

  • To define a plane, you need a point on the plane (P0) and a vector (N) that is perpendicular to it.

  • The dot product of the normal vector (N) and the vector from P0 to any other point on the plane (R - R0) equals zero.

  • Using the formula, A(X - X0) + B(Y - Y0) + C(Z - Z0) = 0, you can find the equation of the plane.

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