3.12: Unit vector and equating column vectors

0606/12/M/J/22 — Question 4 · 5 marks

(a)
Find the unit vector in the same direction as (158)\begin{pmatrix} -15 \\ 8 \end{pmatrix}.
[2]
(b)
Given that (2a5)+(4b123)=4(baa+2b)\begin{pmatrix} 2a \\ -5 \end{pmatrix} + \begin{pmatrix} 4b - 12 \\ 3 \end{pmatrix} = 4\begin{pmatrix} b - a \\ a + 2b \end{pmatrix}, find the values of aa and bb.
[3]