Answer
$\dfrac{8}{3}$
Work Step by Step
The formula to calculate the distance for two vectors is given by:
$d=\dfrac{|u \cdot v|}{|v|}$
Thus, we have $u \cdot v=-2(2)+2(1)-3(2)=-8$
and $|u \times v|=|-8|=8$
Now, $d=\dfrac{|u \cdot v|}{|v|}=\dfrac{8}{ \sqrt {(2)^2+(1)^2+(2)^2}}=\dfrac{8}{ \sqrt {9}}=\dfrac{8}{3}$