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Question 43

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 $OA→\overrightarrow{OA}$ .

[2]

The point $X$ lies on $l$ .

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

find the coordinates of $X$ .

[4]

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

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

[2]

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 43

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 $OA→\overrightarrow{OA}$ .

[2]

The point $X$ lies on $l$ .

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

find the coordinates of $X$ .

[4]

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

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

[2]

Markscheme

Vectors Questions

A Level
Maths
Vectors