Course home

1.13 J: Vectors

Easy Medium Hard

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

Question 13

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

1.13 J: Vectors Questions

A Level
Maths
1.13 J: Vectors

168 exam-style questions on AQA A Level Maths 1.13 J: Vectors, covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems. Each one has a worked solution and a mark scheme showing where the marks go.

1.13 J: Vectors

Question bank

1.13 J: Vectors

Easy Medium Hard

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

Question 13

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

1.13 J: Vectors Questions

A Level
Maths
1.13 J: Vectors