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1.9 Vectors

Question 9

In triangle $O A B$ , $OA⃗=a\vec{OA} = \mathbf{a}$ and $OB⃗=b\vec{OB} = \mathbf{b}$ .

The point $P\,$ divides $AB\,$ in the ratio $A P : P B = 2 : 1$ , and $Q\,$ is the midpoint of $O A$ . The line segments $OP\,$ and $BQ\,$ intersect at $R$ .

Find $OP⃗\vec{OP}$ and $OQ⃗\vec{OQ}$ in terms of $a\mathbf{a}$ and $b\mathbf{b}$ .

[3]

Show that $R\,$ is the midpoint of $BQ\,$ and find the ratio $O R : R P$ .

[4]

Markscheme

1.9 Vectors Questions

A Level
Maths
1.9 Vectors

37 exam-style questions on WJEC A Level Maths 1.9 Vectors, covering 1.9.1 Vectors, 1.9.2 Vectors, 1.9.3 Vectors, 1.9.4 Vectors, and 1.9 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.

1.9 Vectors

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1.9 Vectors

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Question 9

In triangle $O A B$ , $OA⃗=a\vec{OA} = \mathbf{a}$ and $OB⃗=b\vec{OB} = \mathbf{b}$ .

The point $P\,$ divides $AB\,$ in the ratio $A P : P B = 2 : 1$ , and $Q\,$ is the midpoint of $O A$ . The line segments $OP\,$ and $BQ\,$ intersect at $R$ .

Find $OP⃗\vec{OP}$ and $OQ⃗\vec{OQ}$ in terms of $a\mathbf{a}$ and $b\mathbf{b}$ .

[3]

Show that $R\,$ is the midpoint of $BQ\,$ and find the ratio $O R : R P$ .

[4]

Markscheme

1.9 Vectors Questions

A Level
Maths
1.9 Vectors