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Question 34

Relative to a fixed origin $O$ , the path of a high-precision industrial laser cutter $L$ is described by the vector equation

\mathbf{r} = \begin{pmatrix} 3 \\ -2 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 2 \\ -2 \end{pmatrix}

where $λ\lambda$ is a scalar parameter.

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

find $OA→\overrightarrow{OA}$ .

[2]

The point $X$ lies on the path $L$ such that it is the closest point on the path to the origin $O$ .

Find the coordinates of $X$ .

[4]

Points $O$ , $X$ , and $A$ form a triangle $O X A$ .

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

[3]

Markscheme

Vectors Questions

A Level
Maths
Vectors

109 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.

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Question 34

Relative to a fixed origin $O$ , the path of a high-precision industrial laser cutter $L$ is described by the vector equation

\mathbf{r} = \begin{pmatrix} 3 \\ -2 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 2 \\ -2 \end{pmatrix}

where $λ\lambda$ is a scalar parameter.

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

find $OA→\overrightarrow{OA}$ .

[2]

The point $X$ lies on the path $L$ such that it is the closest point on the path to the origin $O$ .

Find the coordinates of $X$ .

[4]

Points $O$ , $X$ , and $A$ form a triangle $O X A$ .

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

[3]

Markscheme

Vectors Questions

A Level
Maths
Vectors