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)

$\frac{5}{\sqrt{22}}$

Answer 2

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 $\left|\frac{-5}{\sqrt{2^{2}+3^{2}+3^{2}}}\right|=\frac{5}{\sqrt{22}}$.