Chapter 1 - Vectors - 1.2 Length and Angle: The Dot Product - Exercises 1.2 - Page 290: 24

:$\theta=135^{\circ}$

We know the following: $\cos\theta=\frac{u\cdot v}{|u||v|}$ Therefore, it follows: $u\cdot v=3(-1)+0(1)=-3$ $|u|=\sqrt{(3^2+0)}=3$ $|v|=\sqrt{((-1)^2+1^2)}=\sqrt{2}$ $\cos\theta=\frac{u.v}{|u||v|}=\frac{-3}{3\sqrt{2}}=\frac{-1}{\sqrt{2}}$ :$\theta=135^{\circ}$