find the angle formed by the intersection of each pair of lines

$\displaystyle 2x+3y-z+9=0$ and $\displaystyle x+2y+4=0$

so the Cartesian coordiantes must be (2,3,-1) and (1,2,0) respectively

therefore the angle between is the dot product/magnitude of line 1x magnitude of line two

so $\displaystyle \frac{(2(1)+3(2)-1(0)}{\sqrt14 \sqrt5}=cos^{-1}(\frac{8}{8.36})=17.02^o$

the book says $\displaystyle 44.2^o$