Relative to a fixed origin OOO, the line lll has vector equation
r=(23−1)+μ(2−12) \mathbf{r} = \begin{pmatrix} 2 \\ 3 \\ -1 \end{pmatrix} + \mu \begin{pmatrix} 2 \\ -1 \\ 2 \end{pmatrix} r=23−1+μ2−12where μ\muμ is a scalar parameter.
Given that OA→\overrightarrow{OA}OA is a unit vector parallel to lll,
find OA→\overrightarrow{OA}OA.
The point XXX lies on lll.
Given that XXX is the point on lll that is closest to the origin,
find the coordinates of XXX.
The points OOO, XXX, and AAA form a triangle OXAOXAOXA.
Find the exact area of triangle OXAOXAOXA.
309 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.