Chapter 1 - Vectors - 1.2 Length and Angle: The Dot Product - Exercises 1.2 - Page 290: 23

Acute

We know the following: $\cos\theta=\frac{u\cdot v}{|u||v|}$ Therefore, it follows: $u\cdot v=1(5)+(2)(6)+3(7)+4(8)=70$ $|u|=\sqrt{((1)^2+(2)^2+(3)^2+(4)^2)}=\sqrt{30}$ $|v|=\sqrt{((5)^2+6^2+7^2+(8)^2)}=\sqrt{174}$ $\cos\theta=\frac{u\cdot v}{|u||v|}=\frac{70}{\sqrt{30}\sqrt{174}}$ This value is between zero and one, so the angle is acute.