The vertex position vectors are \(O=\mathbf0\), \(A=\mathbf p\), \(B=\mathbf p+\mathbf q\), \(C=2\mathbf q\), \(D=2\mathbf q-\mathbf p\), \(E=\mathbf q-\mathbf p\).

(a) (i) \(\overrightarrow{DE}=(\mathbf q-\mathbf p)-(2\mathbf q-\mathbf p)=-\mathbf q\). (ii) \(\overrightarrow{BE}=(\mathbf q-\mathbf p)-(\mathbf p+\mathbf q)=-2\mathbf p\). (iii) \(\overrightarrow{OE}=\mathbf q-\mathbf p\).

(b) On \(OB\), \(\overrightarrow{OG}=t(\mathbf p+\mathbf q)\). On \(DC\), it is \(2\mathbf q-\mathbf p+s\mathbf p\). Comparing independent coefficients gives \(t=2\), \(s=3\), so \(\overrightarrow{OG}=2\mathbf p+2\mathbf q\).