The equation of the plane, the plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0) is mathematically given as
X+Y+Z=18
What is the equation of the plane? the plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0)?
Solve' (0,9,9),(9,0,9),(9,9,0)
Parameters
[tex]\quad A=(0,9,9), \\ \quad B=(9,0,9)\\&c=(9,9,0)\\[/tex]
Generally, the equation for AB is mathematically given as
[tex]&A B=\langle 9,-9,0\rangle\\&\overrightarrow{B C}=\langle 0,9,-9\rangle\\&\text { equation of Plane }\\&(\bar{r}-\overline{O A}) \cdot(\overline{A B} \times \overline{B C})=0\\\\&\overline{A B} \times \overline{B C}=\left|\begin{array}{ccc}i & j & i \\9 & -9 & 0 \\0 & 9 & -9\end{array}\right|\\[/tex]
[tex]&=\{(B)-0)-\hat{j}(-81-0)+k(81-0)\\\\&\overline{A B} \times \overline{B C}=81 \hat{\imath}+81 \hat{\jmath}+81 k)[/tex]
In conclusion, the equation of the plane
81(x-0)+81(y-9)+81(z-9)=0
X+Y+Z=18
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