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Q.
The distance of the origin from the plane through the points $(1, 1, 0)$, $(1, 2, 1)$ and $(-2, 2, -1)$ is
Three Dimensional Geometry
Solution:
The equation of plane is $\begin{vmatrix}x-1&y-1&z\\ 0&1&1\\ -3&1&-1\end{vmatrix}=0$
$\Rightarrow 2x + 3y - 3z = 5$
Distance of origin $\left(0, 0,0\right)$ from the plane is
$\left|\frac{-5}{\sqrt{2^{2}+3^{2}+3^{2}}}\right|=\frac{5}{\sqrt{22}}$.