Triangle area, line–plane angle and distance to a plane

Find the vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$, and hence show that the area of triangle $ABC$ is 1.5 square units.

Find the shortest distance from point $B$ to the line segment $AC$.

A second plane, $\psi$, has the Cartesian equation $2x - 2y - z = -18$.

At what acute angle does the line given by $\tvec{r}(t) = 3\tvec{i} + 2\tvec{j} + 4\tvec{k} + t\left(\tvec{i} - 2\tvec{j} + 2\tvec{k}\right),\ t \in \R$, intersect the plane $\psi$? Give your answer in degrees correct to the nearest degree.

A line $L$ passes through the origin and is normal to the plane $\psi$. The line $L$ intersects $\psi$ at a point $D$.

Write down an equation of the line $L$ in parametric form.

Find the shortest distance from the origin to the plane $\psi$.

Find the coordinates of point $D$.