Points A,B,C A, B, C\,A,B,C and D D\,D have position vectors a=(22)\mathbf{a} = \begin{pmatrix} 2 \\ 2 \end{pmatrix}a=(22), b=(45)\mathbf{b} = \begin{pmatrix} 4 \\ 5 \end{pmatrix}b=(45), c=(84)\mathbf{c} = \begin{pmatrix} 8 \\ 4 \end{pmatrix}c=(84), d=(6k)\mathbf{d} = \begin{pmatrix} 6 \\ k \end{pmatrix}d=(6k)
Find the value of k k\,k for which D D\,D is the midpoint of BCBCBC
Find the two values of k k\,k for which ∣AD⃗∣=25|\vec{AD}| = 2\sqrt{5}∣AD∣=25
Find the value of k k\,k for which ABCD ABCD\,ABCD is a parallelogram.
Hence find the position vector of the point of intersection of the diagonals of ABCDABCDABCD.
284 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.