Points A,B,C A, B, C\,A,B,C and D D\,D have position vectors a=(13)\mathbf{a} = \begin{pmatrix} 1 \\ 3 \end{pmatrix}a=(13), b=(36)\mathbf{b} = \begin{pmatrix} 3 \\ 6 \end{pmatrix}b=(36), c=(75)\mathbf{c} = \begin{pmatrix} 7 \\ 5 \end{pmatrix}c=(75), d=(5k)\mathbf{d} = \begin{pmatrix} 5 \\ k \end{pmatrix}d=(5k)
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.
