Chapter 11 - Practice Exercises - Page 638: 29

$\dfrac{\sqrt {78}}{3}$

The formula to calculate the distance for two vectors is given by: $d=\dfrac{|u \times v|}{|v|}$ Thus, we have $u \times v=\lt -1,3,-4 \gt$ and $|u \times v|=\sqrt{(-1)^2+(3)^2+(-4)^2}=\sqrt {26}$ Now, $d=\dfrac{|u \times v|}{|v|}=\dfrac{\sqrt {26}}{\sqrt{(-1)^2+(1)^2+(1)^2}}=\dfrac{\sqrt {26}}{ \sqrt {3}}=\dfrac{\sqrt {78}}{3}$