Question

The distance of the point $(1,1,1)$ from the plane passing through the points $(2,1,1),(1,2,1)$ and $(1,1,2)$ is

• A. $\frac{1}{\sqrt{3}}$
• B. $1$
• C. $\sqrt{3}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{\sqrt{3}}$

The normal to the plane will be obtained by the cross product of two vectors given, i.e. $(\hat{i}-\hat{j})\times (\hat{i}-\hat{k})=\hat{j}+\hat{k}+\hat{i}$

Thus, the plane equation looks like $x+y+z=d$.

To find $d,$ we substitute the point $(1,2,1)$ and get, $1+2+1=d$.
$\Rightarrow d=4$

Now, the distance of point $(1,1,1)$ will be $\frac{|1+1+1-4|}{\sqrt{3}}=\frac{1}{\sqrt{3}}$