Chapter 11 - Section 11.5 - Lines and Planes in Space - Exercises - Page 631: 43

$\dfrac{5}{3}$

The formula to calculate the distance for two vectors is given by: $d=\dfrac{|u \cdot v|}{|v|}$ Thus, we have $u \cdot v=0(2)+5(1)+0(2)=5$ and $|u \times v|=|5|=5$ Now, $d=\dfrac{|u \cdot v|}{|v|}=\dfrac{5}{ \sqrt {(2)^2+(1)^2+(2)^2}}=\dfrac{5}{ \sqrt {9}}=\dfrac{5}{3}$