OABC OABC\,OABC is a parallelogram, with OA⃗=a\vec{OA} = \mathbf{a}OA=a and OC⃗=c\vec{OC} = \mathbf{c}OC=c.
M M\,M is the midpoint of the diagonal OBOBOB.
Find AC⃗\vec{AC}AC in terms of a\mathbf{a}a and c\mathbf{c}c.
Find OM⃗\vec{OM}OM in terms of a\mathbf{a}a and c\mathbf{c}c, simplifying your answer.
Hence prove that the diagonals of a parallelogram bisect one another.
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.