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 $b\mathbf{b}$ .

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

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 $λ\lambda$ .

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 $b\mathbf{b}$ .

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

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 $λ\lambda$ .

1 Unit 1: Pure Mathematics A

Question 50

Markscheme

1 Unit 1: Pure Mathematics A

Question 50

Markscheme

1 Unit 1: Pure Mathematics A

Question 50

1 Unit 1: Pure Mathematics A Questions

1 Unit 1: Pure Mathematics A

Question 50

1 Unit 1: Pure Mathematics A Questions