Answer
$8.13^{\circ}$ or $0.14$ rad
Work Step by Step
The result of exercise 31 tells us that
${\bf v}=\langle a,\ b \rangle$ is perpendicular to lines $ax+by=c$
${\bf n_{1}}= \langle 3,-4\rangle$ is perpendicular to $3x-4y=3$
${\bf n_{2}}=\langle 1,-1\rangle$ is perpendicular to $x-y=7.$
$\displaystyle \theta=\cos^{-1}(\frac{{\bf n_{1}}\cdot{\bf n_{2}}}{|{\bf n_{1}}||{\bf n_{2}}|})$
$=\displaystyle \cos^{-1}(\frac{3+4}{\sqrt{3+16}\cdot\sqrt{1+1}})$
$=\displaystyle \cos^{-1}(\frac{7}{5\cdot\sqrt{2}})\approx 8.13^{\circ}$ or $0.14$ rad
