Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 236: 72

(a) False. (b) False.

(a) False. Because the unit vector in direction of $v$ is $\frac{v}{\|v\|}$. (b) False. For example, let $u,v\in R^2$ such that $u=(1,0)$ and $v=\left(-1,0\right)$, then $$u\cdot v= -1<0$$ and however one can see that the angle between $u$ and $v$ is $\pi$ which is not acute.