Chapter 1 - Vectors - 1.2 Length and Angle: The Dot Product - Exercises 1.2 - Page 290: 21

Acute

We know the following: $\cos\theta=\frac{u\cdot v}{|u||v|}$ Therefore, it follows: $u\cdot v=0.9(-4.5)+(2.1)(2.6)+1.2(-0.8)=0.45$ $|u|=\sqrt{((0.9)^2+(2.1)^2+(1.2)^2)}=\sqrt{6.66}=2.58$ $|v|=\sqrt{((-4.5)^2+(2.6)^2+(-0.8)^2)}=\sqrt{27.65}=5.26$ So: $\cos\theta=\frac{u.v}{|u||v|}=\frac{0.45}{2.58\times5.26}=0.333$ $\theta = cos^{-1}(.33) =70.7 \ degrees$ The angle is acute.