Urgent: Vectors

$\vec{p}=m\vec{a}+17\vec{b}$
$\vec{q}=3\vec{a}-\vec{b}$

$\vec{p}\bot \vec{q}\Rightarrow \vec{p}\cdot \vec{q}=0$
$\begin{align} \left( m\vec{a}+17\vec{b} \right)\cdot \left( 3\vec{a}-\vec{b} \right)&=0 \\ 3ma\cdot a-ma\cdot b+51a\cdot b-17b\cdot b&=0 \\ 3m|a{{|}^{2}}+\left( 51-m \right)a\cdot b-17|b{{|}^{2}}&=0 \\ 3m|a{{|}^{2}}+\left( 51-m \right)|a||b|\cos 120{}^\circ -17|b{{|}^{2}}&=0 \\ 3m{{\left( 2 \right)}^{2}}+\left( 51-m \right)\left( 2 \right)\left( 5 \right)\left( -\frac{1}{2} \right)-17{{\left( 5 \right)}^{2}}&=0 \\ 12m-255+5m-425&=0 \\ 17m&=680 \\ m&=40 \end{align}$