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
x1 y1 z1 x2 y2 z2 x3 y3 z3
Plug in our point values
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 (y2 z3 - y3 z2 ) + x2 (y3 z1 - y1 z3 ) + x3 (y1 z2 - y2 z1 )
|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
You have 2 free calculationss remaining
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.
What 1 formula is used for the Equation of a Plane Calculator?
Ax + By + Cz + D = 0
|A| = y
1 (z
2 - z
3 ) + y
2 (z
3 - z
1 ) + y
3 (z
1 - z
2 )
|B| = z
1 (x
2 - x
3 ) + z
2 (x
3 - x
1 ) + z
3 (x
1 - x
2 )
|C| = x
1 (y
2 - y
3 ) + x
2 (y
3 - y
1 ) + x
3 (y
1 - y
2 )
|D| = x
1 (y
2 z
3 - y
3 z
2 ) + x
2 (y
3 z
1 - y
1 z
3 ) + x
3 (y
1 z
2 - y
2 z
1 )
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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
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