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Question 11

$OABC\,$ 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]

Markscheme

Vectors Questions

A Level
Maths
Vectors

21 exam-style questions on Edexcel A Level Maths Vectors, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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Question 11

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

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]

Markscheme

Vectors Questions

A Level
Maths
Vectors