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1.13.5 Vectors to solve problems

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Question 39

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

1.13.5 Vectors to solve problems Questions

A Level
Maths
1.13.5 Vectors to solve problems

67 exam-style questions on AQA A Level Maths 1.13.5 Vectors to solve problems. Each one has a worked solution and a mark scheme showing where the marks go.

1.13.5 Vectors to solve problems

Question bank

1.13.5 Vectors to solve 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 39

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

1.13.5 Vectors to solve problems Questions

A Level
Maths
1.13.5 Vectors to solve problems

67 exam-style questions on AQA A Level Maths 1.13.5 Vectors to solve problems. Each one has a worked solution and a mark scheme showing where the marks go.