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1.10 Vectors

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Question 22

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

1.10 Vectors Questions

A Level
Maths
1.10 Vectors

197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.

1.10 Vectors

Question bank

1.10 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 26

Question 22

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

1.10 Vectors Questions

A Level
Maths
1.10 Vectors