Calculate the plane equation with points:
(,,) and (1%2C3%2C5,,) and (9%2C8%2C4,,)
Standard equation for a plane
Ax + By + Cz + D = 0
Calculate Determinants
| A = |
| 1 | y1 | z1 |
| 1 | y2 | z2 |
| 1 | y3 | z3 |
| B = |
| x1 | 1 | z1 |
| x2 | 1 | z2 |
| x3 | 1 | z3 |
| C = |
| x1 | y1 | 1 |
| x2 | y2 | 1 |
| x3 | y3 | 1 |
| D = |
| x1 | y1 | z1 |
| x2 | y2 | z2 |
| x3 | y3 | z3 |
Plug in our point values
| A = |
| 1 | ||
| 1 | ||
| 1 |
| B = |
| 1 | ||
| 1%2C3%2C5 | 1 | |
| 9%2C8%2C4 | 1 |
| C = |
| 1 | ||
| 1%2C3%2C5 | 1 | |
| 9%2C8%2C4 | 1 |
| D = |
| 1%2C3%2C5 | ||
| 9%2C8%2C4 |
Expand the determinant |A|
|A| = y1(z2 - z3) + y2(z3 - z1) + y3(z1 - z2)
|A| =( - ) + ( - ) + ( - )
|A| =(0) + (0) + (0)
|A| =0 + 0 + 0
|A| =0
Expand the determinant |B|
|B| = z1(x2 - x3) + z2(x3 - x1) + z3(x1 - x2)
|B| = (1%2C3%2C5 - 9%2C8%2C4) + (9%2C8%2C4 - ) + ( - 1%2C3%2C5)
|B| =(-8) + (9) + (-1)
|B| =0 + 0 + 0
|B| =0
Expand the determinant |C|
|C| = x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)
|C| = ( - ) + 1%2C3%2C5( - ) + 9%2C8%2C4( - )
|C| =(0) + 1%2C3%2C5(0) + 9%2C8%2C4(0)
|C| =0 + 0 + 0
|C| =0
Expand the determinant |D|
|D| = x1(y2z3 - y3z2) + x2(y3z1 - y1z3) + x3(y1z2 - y2z1)
|D| = (() - ()) + 1%2C3%2C5(() - ()) + 9%2C8%2C4(() - ())
|D| = (0 - 0) + 1%2C3%2C5(0 - 0) + 9%2C8%2C4(0 - 0)
|D| = (0) + 1%2C3%2C5(0) + 9%2C8%2C4(0)
|D| = 0 + 0 + 0
|D| =0
Final Answer
= 0
You have 2 free calculationss remaining
What is the Answer?
= 0
How does the Equation of a Plane Calculator work?
Free Equation of a Plane Calculator - Given three 3-dimensional points, this calculates the equation of a plane that contains those points.
This calculator has 3 inputs.
This calculator has 3 inputs.
What 1 formula is used for the Equation of a Plane Calculator?
Ax + By + Cz + D = 0
|A| = y1(z2 - z3) + y2(z3 - z1) + y3(z1 - z2)
|B| = z1(x2 - x3) + z2(x3 - x1) + z3(x1 - x2)
|C| = x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)
|D| = x1(y2z3 - y3z2) + x2(y3z1 - y1z3) + x3(y1z2 - y2z1)
For more math formulas, check out our Formula Dossier
|A| = y1(z2 - z3) + y2(z3 - z1) + y3(z1 - z2)
|B| = z1(x2 - x3) + z2(x3 - x1) + z3(x1 - x2)
|C| = x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)
|D| = x1(y2z3 - y3z2) + x2(y3z1 - y1z3) + x3(y1z2 - y2z1)
For more math formulas, check out our Formula Dossier
What 6 concepts are covered in the Equation of a Plane Calculator?
- determinant
- value computed from a square matrix
det(A) or |A| - equation
- a statement declaring two mathematical expressions are equal
- equation of a plane
- formula to graph the points in a plane
Ax + By + Cz + D = 0 - matrix
- a rectangular array of numbers or symbols which are generally arranged in rows and columns
- plane
- a flat, two-dimensional surface that extends indefinitely
- point
- an exact location in the space, and has no length, width, or thickness
Example calculations for the Equation of a Plane Calculator
Equation of a Plane Calculator Video
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