Algebra 1, Section 7.08
2 answers:
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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 .