Question

Find the distance of the plane $\overrightarrow{r}\cdot (2\hat{i}+\hat{j}+2\hat{k})=6$ from the origin.

Answer 1

Let the vector $\overrightarrow{r}$ be $x\hat{i}+y\hat{j}+z\hat{k}$

The equation of plane will be $2x+y+2z-6=0$

Therefore the distance from origin to given plane is $\frac{|2\left(0\right)+\left(0\right)+2\left(0\right)-6|}{\sqrt{2^2+1^2+2^2}}=\frac{6}{3}=2$