Let $\vec F= x\,\mathit{\vec i}+\left(x+y\right)\,\mathit{\vec j}+\left(x-y+z\right)\,\mathit{\vec k}$. Let the line $l$ be $x = 3+2t$, $y = 5-t$, $z = t-3$.

(a) Find a point $P = (x_0, y_0, z_0)$ where $\vec F$ is parallel to $l$.
$P =$

Find a point $Q = (x_1,y_1,z_1)$ at which $\vec F$ and $l$ are perpendicular.
$Q =$

Give an equation for the set of all points at which $\vec F$ and $l$ are perpendicular.
equation: