Answer:
Hence, none of the options presented are valid. The plane is represented by .
Step-by-step explanation:
The general equation in rectangular form for a 3-dimension plane is represented by:
Where:
, , - Orthogonal inputs.
, , , - Plane constants.
The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)
For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:
xy-plane (2, 0, 0) and (0, 2, 0)
Where:
- Slope, dimensionless.
, - Initial and final values for the independent variable, dimensionless.
, - Initial and final values for the dependent variable, dimensionless.
- x-Intercept, dimensionless.
If , , and , then:
Slope
x-Intercept
The equation of the line in the xy-plane is or , which is equivalent to .
yz-plane (0, 2, 0) and (0, 0, 3)
Where:
- Slope, dimensionless.
, - Initial and final values for the independent variable, dimensionless.
, - Initial and final values for the dependent variable, dimensionless.
- y-Intercept, dimensionless.
If , , and , then:
Slope
y-Intercept
The equation of the line in the yz-plane is or .
xz-plane (2, 0, 0) and (0, 0, 3)
Where:
- Slope, dimensionless.
, - Initial and final values for the independent variable, dimensionless.
, - Initial and final values for the dependent variable, dimensionless.
- z-Intercept, dimensionless.
If , , and , then:
Slope
x-Intercept
The equation of the line in the xz-plane is or
After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:
, , ,
Hence, none of the options presented are valid. The plane is represented by .