Relative to a fixed origin OOO, the path of a high-precision industrial laser cutter LLL is described by the vector equation
r=(3−24)+λ(12−2)\mathbf{r} = \begin{pmatrix} 3 \\ -2 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 2 \\ -2 \end{pmatrix}r=3−24+λ12−2
where λ\lambdaλ is a scalar parameter.
Given that OA→\overrightarrow{OA}OA is a unit vector parallel to the path LLL,
find OA→\overrightarrow{OA}OA.
The point XXX lies on the path LLL such that it is the closest point on the path to the origin OOO.
Find the coordinates of XXX.
Points OOO, XXX, and AAA form a triangle OXAOXAOXA.
Determine the exact area of triangle OXAOXAOXA.
Practise Edexcel A Level Maths Vectors with exam-style questions for A Level Maths. 100 questions covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.