Vectors

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$OABC\,$ is a parallelogram with $OA⃗=a\vec{OA} = \mathbf{a}$ and $OC⃗=c\vec{OC} = \mathbf{c}$ . $M\,$ is the midpoint of $O B$ .

Diagram of a parallelogram OABC. Vertex O is at the bottom-left, A is at the top-left, B is at the top-right, and C is at the bottom-right. A diagonal line segment connects O and B. Point M is marked as the midpoint of this diagonal OB.

Find in terms of $a\mathbf{a}$ and $c\mathbf{c}$ , simplifying your answers.

(i) $AC⃗\vec{AC}$

(ii) $OM⃗\vec{OM}$

[3]

Hence prove that the diagonals of a parallelogram bisect one another.

[4]

Vectors Questions

Practise Edexcel AS Level Maths Vectors with exam-style questions for AS Level Maths. 15 questions covering 11.1 Vectors, 11.2 Representing Vectors, 11.3 Magnitude and Direction, 11.4 Position Vectors, 11.5 Solving Geometric Problems, and 11.6 Modelling with Vectors, matched to the Edexcel AS Level Maths (8MA0) specification and written in Paper 1 and Paper 2 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.