Question 48 – 12.3 Solving Geometric Problems - Questions

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

\mathbf{r} = \begin{pmatrix} 2 \\ 3 \\ -1 \end{pmatrix} + \mu \begin{pmatrix} 2 \\ -1 \\ 2 \end{pmatrix}

where $μ\mu$ is a scalar parameter.

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

find $OA→\overrightarrow{OA}$ .

The point $X$ lies on $l$ .

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

find the coordinates of $X$ .

The points $O$ , $X$ , and $A$ form a triangle $O X A$ .

Find the exact area of triangle $O X A$ .