Course home

1.9 Vectors

Easy Medium Hard

1 2 3 4 5 6 7 8 9

Question 5

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 $2 : 3$ , and $Q\,$ is the midpoint of $O B$ .

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

[2]

Find $QP⃗\vec{QP}$ in terms of $a\mathbf{a}$ and $b\mathbf{b}$ , simplifying your answer.

[2]

The point $R\,$ lies on the line $OA\,$ produced, with $OR⃗=λa\vec{OR} = \lambda\mathbf{a}$ . Given that $Q$ , $P\,$ and $R\,$ are collinear, find the value of $λ\lambda$ .

[3]

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

Question bank

1.9 Vectors

Easy Medium Hard

1 2 3 4 5 6 7 8 9

Question 5

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 $2 : 3$ , and $Q\,$ is the midpoint of $O B$ .

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

[2]

Find $QP⃗\vec{QP}$ in terms of $a\mathbf{a}$ and $b\mathbf{b}$ , simplifying your answer.

[2]

The point $R\,$ lies on the line $OA\,$ produced, with $OR⃗=λa\vec{OR} = \lambda\mathbf{a}$ . Given that $Q$ , $P\,$ and $R\,$ are collinear, find the value of $λ\lambda$ .

[3]

Markscheme

1.9 Vectors Questions

A Level
Maths
1.9 Vectors