Problems from Distance between a straight line and a plane in space

Calculate the distance between the straight line and the plane:

$r : (x, y, z) = (2, 1, 0) + k \cdot (1, 4 - 3)$

$π : x + y + 2 z - 1 = 0$

See development and solution

Development:

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 $d (r, π) = 0$ .

Solution:

$d (r, π) = 0$

Hide solution and development