Calculate the plane equation with points:
(,,) and (1,3,5) and (9,8,4)
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 | 3 | 5 |
| 1 | 8 | 4 |
| B = |
| 1 | ||
| 1 | 1 | 5 |
| 9 | 1 | 4 |
| C = |
| 1 | ||
| 1 | 3 | 1 |
| 9 | 8 | 1 |
| D = |
| 1 | 3 | 5 |
| 9 | 8 | 4 |
Expand the determinant |A|
|A| = y1(z2 - z3) + y2(z3 - z1) + y3(z1 - z2)
|A| =(5 - 4) + 3(4 - ) + 8( - 5)
|A| =(1) + 3(4) + 8(-5)
|A| =0 + 12 + -40
|A| =-28
Expand the determinant |B|
|B| = z1(x2 - x3) + z2(x3 - x1) + z3(x1 - x2)
|B| = (1 - 9) + 5(9 - ) + 4( - 1)
|B| =(-8) + 5(9) + 4(-1)
|B| =0 + 45 + -4
|B| =41
Expand the determinant |C|
|C| = x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)
|C| = (3 - 8) + 1(8 - ) + 9( - 3)
|C| =(-5) + 1(8) + 9(-3)
|C| =0 + 8 + -27
|C| =-19
Expand the determinant |D|
|D| = x1(y2z3 - y3z2) + x2(y3z1 - y1z3) + x3(y1z2 - y2z1)
|D| = (3(4) - (8)5) + 1(8() - ()4) + 9((5) - (3))
|D| = (12 - 40) + 1(0 - 0) + 9(0 - 0)
|D| = (-28) + 1(0) + 9(0)
|D| = 0 + 0 + 0
|D| =0
Final Answer
-28x + 41y - 19z = 0
What is the Answer?
-28x + 41y - 19z = 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)
|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)
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
