Problem

Relative to a fixed origin $O$, the line $l$ has equation

$$\mathbf{r}= \begin{pmatrix} 1\\4\\-10 \end{pmatrix} +\lambda \begin{pmatrix} 4\\2\\-9 \end{pmatrix} \qquad \text{where }\lambda\text{ is a scalar parameter}$$

Given that $\overrightarrow{OA}$ is a unit vector parallel to $l$,

(a) find $\overrightarrow{OA}$

The point $X$ lies on $l$.

Given that $X$ is the point on $l$ that is closest to the origin,

(b) find the coordinates of $X$.

The points $O$, $X$ and $A$ form the triangle $OXA$.

(c) Find the exact area of triangle $OXA$.