\(\mathbf a=\binom{-2}{3},\quad\mathbf b=\binom{2}{-7},\quad\mathbf c=\binom{-10}{21}\).

(a(i)) Find 2a + b. [1]

(a(ii)) Find the magnitude of b. [2]

(a(iii)) ma + nb = c. Find m and n, showing all working. [6]

\(\overrightarrow{OP}=\mathbf p,\quad\overrightarrow{OQ}=\mathbf q\). OX:XP = OY:YQ = 3:2.

(b(i)) Find \(\overrightarrow{PQ}\). [1]

(b(ii)) Find \(\overrightarrow{XY}\). [1]

(b(iii)) Complete: XY and PQ are …; OXY and OPQ are …; area OXY : area OPQ = … . [3]