3.10: Opposite direction vector and linear combination

0606/11/M/J/22 — Question 5 · 5 marks

(a)
Find the vector which is in the opposite direction to (158)\begin{pmatrix} 15 \\ -8 \end{pmatrix} and has a magnitude of 8.58.5.
[2]
(b)
Find the values of aa and bb such that 5(3ab)+(2a+12)=6(a+b2)5\begin{pmatrix} 3a \\ b \end{pmatrix} + \begin{pmatrix} 2a + 1 \\ 2 \end{pmatrix} = 6\begin{pmatrix} a + b \\ 2 \end{pmatrix}.
[3]