ข้อ 32
$u=(2,-5)\ \ \ v=(1,2)\ \ \ \ w=(a,b)$
$u\cdot w=2a-5b=-11$----------(1)
$v\cdot w=a+2b=8$--------------(2)
จาก (1),(2) -------> $a=2,b=3$------>$w=(2,3)$
ให้ $z=(5,1)$------->$w\cdot z=13$
$|w||z|=(\sqrt{13})(\sqrt{26})=13\sqrt{2}$
$\because w\cdot z=|w||z|cos\theta$
$\therefore 13=13\sqrt{2}cos\theta$
$cos\theta=\frac{1}{\sqrt{2}}$---->$\theta=45$
$tan\theta+sin2\theta=tan45+sin90=2$