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=(56)\mathbf{b} = \begin{pmatrix} 5 \\ 6 \end{pmatrix}b=(56), c=(114)\mathbf{c} = \begin{pmatrix} 11 \\ 4 \end{pmatrix}c=(114), d=(8k)\mathbf{d} = \begin{pmatrix} 8 \\ k \end{pmatrix}d=(8k)
Find the value of k k\,k for which D D\,D is the midpoint of BCBCBC
Find AD⃗\vec{AD}AD in terms of kkk.
Hence find the two values of k k\,k for which ∣AD⃗∣=210|\vec{AD}| = 2\sqrt{10}∣AD∣=210
Find the value of k k\,k for which ABCD ABCD\,ABCD is a parallelogram.
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.