Answer
$\dfrac{\sqrt {78}}{3}$
Work Step by Step
The distance formula for two vectors $p$ and $q$ can be calculated as:
$d=\dfrac{|p \times q|}{|p|}$
Thus, we have: $p \times q=\lt -1,3,-4 \gt$
and $|p \times q|=\sqrt{(-1)^2+(3)^2+(-4)^2}=\sqrt {26}$
Thus, $d=\dfrac{\sqrt {26}}{\sqrt{(-1)^2+(1)^2+(1)^2}}=\dfrac{\sqrt {26}}{ \sqrt {3}}=\dfrac{\sqrt {78}}{3}$
