Two straight lines $$r$$ and $$s$$ are perpendicular if the scalar product of its governing vectors is zero: $$$r \ \text{ perpendicular to } \ s \Leftrightarrow \vec{u}\cdot\vec{v}=0$$$

The straight lines:

$$$r:(x,y,z)=(0,0,0)+k\cdot(3, 2, 4) \quad \text{ and } \\ s:(x,y,z)=(1,1,3)+ k\cdot(0,2,-1)$$$

are perpendicular since its governing vectors verify: $$$(3, 2, 4)\cdot(0, 2, -1) = 0$$$