Question

The distance of the origin from the plane through the points $(1,1,0)$, $(1,2,1)$ and $(-2,2,-1)$ is

• A. $\frac{3}{\sqrt{11}}$
• B. $\frac{5}{\sqrt{22}}$
• C. $3$
• D. $\frac{4}{\sqrt{22}}$

Answer 1

Answer: (B)

The equation of plane is $\left|\begin{array}{ccc}x-1& y-1& z\\ 0& 1& 1\\ -3& 1& -1\end{array}\right|=0$
$\Rightarrow 2x+3y-3z=5$
Distance of origin $\left(0,0,0\right)$ from the plane is
$\left|\frac{-5}{\sqrt{2^2+3^2+3^2}}\right|=\frac{5}{\sqrt{22}}$.