Distance between a straight line and a plane in space
Calculate the distance between the straight line and the plane:
$$r:(x,y,z)=(2,1,0)+k\cdot(1,4-3)$$
$$\pi:x+y+2z-1=0$$
Let's consider the governing vector of the straight line, $\vec{v}=(1,4,-3)$, and the normal vector of the plane, $\vec{n}=(1,1,2)$ and we do the scalar product: $$(1, 4, -3)\cdot(1, 1, 2) = -1 \neq 0$$ Therefore the straight line and the plane are not parallel and $\text{d}(r,\pi)=0$.
$\text{d}(r,\pi) = 0$