Equation of a Plane Passing through three Point Calculator

$\color{red} \bold{Related \space Calculators}$

Distance of a point from a Line
Distance of a point from a Plane
Angle between line and Plane
Angle between two Planes
Normal to the Plane passing through the three points
Equation of a Plane through a Point & a Normal Vector

$\bold{Table \space of \space Contents}$

• 1. Introduction to the Equation of the Plane containing 3-points
• 2. What is the Formulae used ?
• 3. How do I calculate the Equation of the Plane containing 3-points?
• 4. Why choose our Equation of the Plane containing 3-points Calculator?
• 5. A Video for explaining this concept
• 6. How to use this calculator ?
• 7. Solved Examples
• 8. Frequently Asked Questions (FAQs)
• 9. What are the real-life applications?
• 10. Conclusion

1. Introduction to the Equation of the Plane containing 3-points

Welcome to the realm of geometry, where points in space come together to form planes, the building blocks of three-dimensional worlds. In this blog, we'll discover the equation of a plane that passes through three points. Whether you're a student exploring the depths of geometry or someone intrigued by the spatial magic around us, let's unravel the secrets of plane equations in plain English.
$\bold{Definition}$
The equation of a plane through three points is a mathematical representation that encapsulates the geometric relationships between these points. This equation allows us to define and understand the orientation of an aircraft in three-dimensional space.

2. What is the Formulae used?

The general equation of a plane in three-dimensional space is given by: Ax + By + Cz = D, where A, B, and C are coefficients determined by the normal vector of the plane, and D is a constant determined by the specific points the plane passes through.

3. How do I calculate the Equation of the Plane containing 3-points?

Identify the coordinates of the three points as A, B, C.
Fins the $\vec{AB}$ = B - A and $\vec{AC}$ = C - A.
Find the cross-product of $\vec{AB}$ and $\vec{AC}$.
Use any of the 1 given point and normal vector to obtain the plane equation.

4. Why choose our Equation of the Plane containing a 3-point Calculator?

$\bold{Easy \space \space to \space Use}$
Our calculator page provides a user-friendly interface that makes it accessible to both students and professionals. You can quickly input your square matrix and obtain the matrix of minors within a fraction of a second.

$\bold{Time \space Saving \space By \space automation}$
Our calculator saves you valuable time and effort. You no longer need to manually calculate each cofactor, making complex matrix operations more efficient.

$\bold{Accuracy \space and \space Precision}$
Our calculator ensures accurate results by performing calculations based on established mathematical formulas and algorithms. It eliminates the possibility of human error associated with manual calculations.

$\bold{Versatility}$
Our calculator can handle all input values like integers, fractions, or any real number.

$\bold{Complementary \space Resources}$
Alongside this calculator, our website offers additional calculators related to Pre-algebra, Algebra, Precalculus, Calculus, Coordinate geometry, Linear algebra, Chemistry, Physics, and various algebraic operations. These calculators can further enhance your understanding and proficiency.

5. A video based on the concept of how to find the Equation of the Plane containing 3-points.

6. How to use this calculator

This calculator will help you to find the Equation of the Plane containing 3 points.
In the given input boxes, you must put the value of the coordinates of points A, B, and C.
After clicking the Calculate button, a step-by-step solution will be displayed on the screen.
You can access, download, and share the solution.

7. Solved Examples

$\bold{Question}$
Find the equation of the plane containing three points as A (1, 2, 3), B (4, 0, 3), and C (5, -1, 4).
$\bold{Solution}$
$\vec{AB}$ = (4, 0, 3) - (1, 2, 3) = (3, -2, 0)
$\vec{AC}$ = (5, -1, 4) - (1, 2, 3) = (4, -3, 1)
$\vec{AB}$ X $\vec{AC}$ = Normal to the plane = (-1, -2, -1)
Equation of the plane: $(-1)(x - 1) + (-2)(y - 2) + (-1)(z - 3)$ = 0
Obtained equation of the plane is (-x - 2y - z + 8 = 0).

8. Frequently Asked Questions (FAQs)

What if the three points are collinear?

The plane equation is undefined for collinear points.

Can I use more than three points to find the plane equation?

No, three non-collinear points are sufficient to define a plane uniquely.

Can the coefficients A, B, and C be zero?

Yes, but not all three simultaneously. At least one of them must be non-zero.

What if the normal vector is parallel to one of the coordinate axes?

In this case, the equation can be simplified, and one of the coefficients (A, B, or C) becomes zero.

Are there alternative methods to find the equation of a plane?

While other methods exist, cross-products are commonly used for simplicity.

9. What are the real-life applications?

Understanding the equation of a plane is essential in architecture and engineering for designing structures, in computer graphics for rendering realistic scenes, and in physics for modeling surfaces in simulations.

10. Conclusion

Mastering the calculation of the equation of a plane through three points unlocks the language of spatial relationships. From crafting 3D graphics to designing structural elements, this concept plays a pivotal role in shaping our understanding of the three-dimensional world. So, the next time you ponder the orientation of a plane defined by points, remember that the equation is the key to unveiling the geometric harmony around us!

This blog is written by Neetesh Kumar

If you have any suggestions regarding the improvement of the content of this page, please write to me at My Official Email Address: [email protected]

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