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12.3 Solving Geometric Problems

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Question 31

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

12.3 Solving Geometric Problems Questions

A Level
Maths
12.3 Solving Geometric Problems

55 exam-style questions on Edexcel A Level Maths 12.3 Solving Geometric Problems. Each one has a worked solution and a mark scheme showing where the marks go.

12.3 Solving Geometric Problems

Question bank

12.3 Solving Geometric Problems

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Question 31

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

12.3 Solving Geometric Problems Questions

A Level
Maths
12.3 Solving Geometric Problems

55 exam-style questions on Edexcel A Level Maths 12.3 Solving Geometric Problems. Each one has a worked solution and a mark scheme showing where the marks go.