Answer
$\dfrac{19}{5}$
Work Step by Step
The distance formula for two vectors can be calculated as:
$d=\dfrac{|p \cdot q|}{|q|}$
Now, $p \cdot q=0(0)-4(4)+1(3)=-19$
and $|p \times q|=|-19|=19$
Thus, $d=\dfrac{19}{ \sqrt {(0)^2+(4)^2+(3)^2}}=\dfrac{19}{ \sqrt {16+9}}$
or, $=\dfrac{19}{ \sqrt {25}}$
or, $=\dfrac{19}{5}$
